diff --git a/pretraining/mathematica/geometry/solids/10668.txt b/pretraining/mathematica/geometry/solids/10668.txt new file mode 100644 index 0000000000000000000000000000000000000000..51fd342fef8878e6420e8229ac44f66e6337b60b --- /dev/null +++ b/pretraining/mathematica/geometry/solids/10668.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.736 & 0.925 & 0.081 \\ + 0.106 & 0.104 & 0.262 \\ + 0.356 & 0.414 & 0.561 \\ + 0.569 & 0.417 & 0.846 \\ + 0.894 & 0.081 & 0.297 \\ + 0.825 & 0.454 & 0.873 \\ + 0.53 & 0.131 & 0.856 \\ + 0.191 & 0.586 & 0.078 \\ + 0.289 & 0.926 & 0.16 \\ + 0.242 & 0.018 & 0.568 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $2.11$ +Volume: $0.2$ +Solid Angle: $1.07$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/11037.txt b/pretraining/mathematica/geometry/solids/11037.txt new file mode 100644 index 0000000000000000000000000000000000000000..945dbb7518e41953bbc10b9c23d4110c30f4579a --- /dev/null +++ b/pretraining/mathematica/geometry/solids/11037.txt @@ -0,0 +1,17 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.17 & 0.902 & 0.73 \\ + 0.754 & 0.47 & 0.504 \\ + 0.843 & 0.487 & 0.276 \\ + 0.102 & 0.91 & 0.587 \\ + 0.192 & 0.622 & 0.978 \\ + 0.32 & 0.282 & 0.046 \\ + 0.524 & 0.533 & 0.884 \\ + 0.244 & 0.76 & 0.167 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $2.13$ +Surface Area: $1.34$ +Volume: $0.09$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/11879.txt b/pretraining/mathematica/geometry/solids/11879.txt new file mode 100644 index 0000000000000000000000000000000000000000..d6c591249ff2832b31eb4920b73342f4cbe4adb6 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/11879.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.739 & 0.564 & 0.677 \\ + 0.126 & 0.832 & 0.213 \\ + 0.777 & 0.836 & 0.194 \\ + 0.001 & 0.88 & 0.779 \\ + 0.905 & 0.024 & 0.921 \\ + 0.215 & 0.223 & 0.033 \\ + 0.846 & 0.589 & 0. \\ + 0.594 & 0.78 & 0.741 \\ + 0.728 & 0.023 & 0.947 \\ + 0.136 & 0.204 & 0.156 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.29$ +Solid Angle: $6.01$ +Surface Area: $2.59$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/12094.txt b/pretraining/mathematica/geometry/solids/12094.txt new file mode 100644 index 0000000000000000000000000000000000000000..05d6bb40d8d2872df4e8930d00b60f3879633fff --- /dev/null +++ b/pretraining/mathematica/geometry/solids/12094.txt @@ -0,0 +1,14 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.62 & 0.689 & 0.79 \\ + 0.242 & 0.833 & 0.378 \\ + 0.921 & 0.69 & 0.418 \\ + 0.732 & 0.436 & 0.388 \\ + 0.168 & 0.004 & 0.185 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $0.96$ +Solid Angle: $0.94$ +Volume: $0.04$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/13278.txt b/pretraining/mathematica/geometry/solids/13278.txt new file mode 100644 index 0000000000000000000000000000000000000000..23f9a02115191720d14347cf83bd9d22a4fd3c6d --- /dev/null +++ b/pretraining/mathematica/geometry/solids/13278.txt @@ -0,0 +1,18 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.156 & 0.249 & 0.445 \\ + 0.755 & 0.429 & 0.09 \\ + 0.409 & 0.339 & 0.574 \\ + 0.506 & 0.464 & 0.22 \\ + 0.399 & 0.577 & 0.543 \\ + 0.118 & 0.003 & 0.165 \\ + 0.745 & 0.086 & 0.212 \\ + 0.99 & 0.964 & 0.523 \\ + 0.949 & 0.681 & 0.32 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.27$ +Solid Angle: $1.36$ +Volume: $0.07$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/14645.txt b/pretraining/mathematica/geometry/solids/14645.txt new file mode 100644 index 0000000000000000000000000000000000000000..e1bb941d3d00a0daf6645a3598ac2061020b6a86 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/14645.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.228 & 0.969 & 0.355 \\ + 0.522 & 0.006 & 0.568 \\ + 0.444 & 0.643 & 0.662 \\ + 0.831 & 0.89 & 0.258 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.02$ +Solid Angle: $0.34$ +Surface Area: $0.75$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/16212.txt b/pretraining/mathematica/geometry/solids/16212.txt new file mode 100644 index 0000000000000000000000000000000000000000..de702f395f99dfce36293b5f13290535601d0d15 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/16212.txt @@ -0,0 +1,20 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.48 & 0.592 & 0.902 \\ + 0.329 & 0.339 & 0.848 \\ + 0.7 & 0.245 & 0.945 \\ + 0.787 & 0.141 & 0.448 \\ + 0.483 & 0.538 & 0.202 \\ + 0.177 & 0.313 & 0.029 \\ + 0.718 & 0.471 & 0.744 \\ + 0.553 & 0.513 & 0.311 \\ + 0.687 & 0.232 & 0.351 \\ + 0.555 & 0.248 & 0.9 \\ + 0.171 & 0.61 & 0.64 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.24$ +Solid Angle: $1.96$ +Volume: $0.09$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/19529.txt b/pretraining/mathematica/geometry/solids/19529.txt new file mode 100644 index 0000000000000000000000000000000000000000..c74ef3965ac0a14bec8844be1dfe832c65d9059a --- /dev/null +++ b/pretraining/mathematica/geometry/solids/19529.txt @@ -0,0 +1,14 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.819 & 0.976 & 0.378 \\ + 0.895 & 0.63 & 0.878 \\ + 0.337 & 0.054 & 0.48 \\ + 0.732 & 0.434 & 0.58 \\ + 0.747 & 0.577 & 0.894 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $0.65$ +Solid Angle: $0.16$ +Volume: $0.02$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/21064.txt b/pretraining/mathematica/geometry/solids/21064.txt new file mode 100644 index 0000000000000000000000000000000000000000..06dafc7703060654aef0a57fc942657a50914436 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/21064.txt @@ -0,0 +1,18 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.116 & 0.739 & 0.243 \\ + 0.199 & 0.641 & 0.226 \\ + 0.628 & 0.911 & 0.113 \\ + 0.718 & 0.222 & 0.919 \\ + 0.328 & 0.782 & 0.951 \\ + 0.86 & 0.465 & 0.625 \\ + 0.348 & 0.555 & 0.33 \\ + 0.719 & 0.971 & 0.607 \\ + 0.262 & 0.798 & 0.569 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.43$ +Solid Angle: $1.26$ +Volume: $0.1$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/21085.txt b/pretraining/mathematica/geometry/solids/21085.txt new file mode 100644 index 0000000000000000000000000000000000000000..00d39dd549892b6a18c52e07245ed4fcce380947 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/21085.txt @@ -0,0 +1,15 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.814 & 0.614 & 0.448 \\ + 0.237 & 0.776 & 0.994 \\ + 0.171 & 0.199 & 0.352 \\ + 0.169 & 0.494 & 0.465 \\ + 0.398 & 0.882 & 0.052 \\ + 0.258 & 0.425 & 0.065 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.22$ +Solid Angle: $0.95$ +Volume: $0.08$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/22351.txt b/pretraining/mathematica/geometry/solids/22351.txt new file mode 100644 index 0000000000000000000000000000000000000000..a80340c0a1de1edfdfcced5ef39740a33a2c594e --- /dev/null +++ b/pretraining/mathematica/geometry/solids/22351.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.858 & 0.815 & 0.806 \\ + 0.933 & 0.154 & 0.64 \\ + 0.833 & 0.906 & 0.606 \\ + 0.019 & 0.457 & 0.189 \\ + 0.228 & 0.62 & 0.107 \\ + 0.156 & 0.949 & 0.238 \\ + 0.302 & 0.21 & 0.504 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $1.18$ +Volume: $0.09$ +Surface Area: $1.55$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/23039.txt b/pretraining/mathematica/geometry/solids/23039.txt new file mode 100644 index 0000000000000000000000000000000000000000..9a9eccffec339540daafc3707c893a8bf9175142 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/23039.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.224 & 0.718 & 0.856 \\ + 0.729 & 0.518 & 0.73 \\ + 0.713 & 0.962 & 0.412 \\ + 0.311 & 0.474 & 0.633 \\ + 0.287 & 0.591 & 0.381 \\ + 0.271 & 0.846 & 0.368 \\ + 0.332 & 0.793 & 0.311 \\ + 0.55 & 0.845 & 0.957 \\ + 0.812 & 0.543 & 0.898 \\ + 0.36 & 0.352 & 0.495 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.03$ +Volume: $0.07$ +Solid Angle: $1.58$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/24086.txt b/pretraining/mathematica/geometry/solids/24086.txt new file mode 100644 index 0000000000000000000000000000000000000000..02d59154b3c69938cf8521d5ffd91dad2eb5356a --- /dev/null +++ b/pretraining/mathematica/geometry/solids/24086.txt @@ -0,0 +1,5 @@ +Problem: +A sphere centered at $\{-4.764,-5.611,8.819\}$ has radius $9.292$. Estimate the sphere's surface area and volume. +Answer: +Volume: $3360.74$ +Surface Area: $1085.03$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/25998.txt b/pretraining/mathematica/geometry/solids/25998.txt new file mode 100644 index 0000000000000000000000000000000000000000..b26b7ecb89c059af3fc45327531faa7819b4afe3 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/25998.txt @@ -0,0 +1,21 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.733 & 0.972 & 0.788 \\ + 0.248 & 0.661 & 0.567 \\ + 0.848 & 0.125 & 0.461 \\ + 0.206 & 0.789 & 0.009 \\ + 0.861 & 0.151 & 0.418 \\ + 0.212 & 0.018 & 0.58 \\ + 0.948 & 0.107 & 0.77 \\ + 0.25 & 0.198 & 0.061 \\ + 0.267 & 0.215 & 0.667 \\ + 0.756 & 0.183 & 0.278 \\ + 0.863 & 0.484 & 0.299 \\ + 0.559 & 0.762 & 0.327 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $2.21$ +Solid Angle: $0.9$ +Volume: $0.23$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/26772.txt b/pretraining/mathematica/geometry/solids/26772.txt new file mode 100644 index 0000000000000000000000000000000000000000..e3c2746fe967a567f247393141754dae454d5f37 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/26772.txt @@ -0,0 +1,17 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.95 & 0.889 & 0.556 \\ + 0.825 & 0.27 & 0.063 \\ + 0.591 & 0.831 & 0.399 \\ + 0.023 & 0.022 & 0.853 \\ + 0.101 & 0.482 & 0.285 \\ + 0.063 & 0.014 & 0.989 \\ + 0.979 & 0.577 & 0.815 \\ + 0.558 & 0.987 & 0.202 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $1.39$ +Surface Area: $2.23$ +Volume: $0.19$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/27895.txt b/pretraining/mathematica/geometry/solids/27895.txt new file mode 100644 index 0000000000000000000000000000000000000000..0e9bfe6e17e2335829079c82609fc2a4ce531d83 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/27895.txt @@ -0,0 +1,17 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.408 & 0.238 & 0.887 \\ + 0.165 & 0.409 & 0.634 \\ + 0.658 & 0.623 & 0.067 \\ + 0.848 & 0.696 & 0.75 \\ + 0.693 & 0.965 & 0.81 \\ + 0.47 & 0.169 & 0.164 \\ + 0.193 & 0.92 & 0.038 \\ + 0.672 & 0.212 & 0.776 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.87$ +Volume: $0.18$ +Solid Angle: $1.72$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/28130.txt b/pretraining/mathematica/geometry/solids/28130.txt new file mode 100644 index 0000000000000000000000000000000000000000..603a0361f29297cff64e4f34df1066bbee2a43fa --- /dev/null +++ b/pretraining/mathematica/geometry/solids/28130.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.751 & 0.257 & 0.101 \\ + 0.325 & 0.121 & 0.358 \\ + 0.686 & 0.631 & 0.139 \\ + 0.35 & 0.392 & 0.253 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $0.15$ +Surface Area: $0.28$ +Volume: $0.$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/2913.txt b/pretraining/mathematica/geometry/solids/2913.txt new file mode 100644 index 0000000000000000000000000000000000000000..70e510a3f674adfa0cf663c27bc543656c488cd7 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/2913.txt @@ -0,0 +1,14 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.099 & 0.493 & 0.106 \\ + 0.927 & 0.376 & 0.684 \\ + 0.79 & 0.946 & 0.22 \\ + 0.895 & 0.658 & 0.75 \\ + 0.201 & 0.911 & 0.714 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $0.43$ +Volume: $0.08$ +Surface Area: $1.29$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/3021.txt b/pretraining/mathematica/geometry/solids/3021.txt new file mode 100644 index 0000000000000000000000000000000000000000..8c54aea96ab11392a48bfdc83fdee31bd96d1d81 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/3021.txt @@ -0,0 +1,15 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.221 & 0.616 & 0.279 \\ + 0.312 & 0.956 & 0.001 \\ + 0.971 & 0.43 & 0.448 \\ + 0.888 & 0.725 & 0.215 \\ + 0.225 & 0.279 & 0.084 \\ + 0.982 & 0.072 & 0.82 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $2.41$ +Surface Area: $1.34$ +Volume: $0.06$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/3200.txt b/pretraining/mathematica/geometry/solids/3200.txt new file mode 100644 index 0000000000000000000000000000000000000000..56f0050fda13fca759dc717aa13524f1fb9cc5f1 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/3200.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.795 & 0.305 & 0.258 \\ + 0.609 & 0.393 & 0.313 \\ + 0.572 & 0.501 & 0.322 \\ + 0.916 & 0.449 & 0.342 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $0.08$ +Volume: $0.$ +Solid Angle: $0.16$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/32693.txt b/pretraining/mathematica/geometry/solids/32693.txt new file mode 100644 index 0000000000000000000000000000000000000000..9802318323be3908973c35ce8a5de2e8dbc8339e --- /dev/null +++ b/pretraining/mathematica/geometry/solids/32693.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.716 & 0.974 & 0.969 \\ + 0.539 & 0.127 & 0.175 \\ + 0.237 & 0.913 & 0.894 \\ + 0.584 & 0.742 & 0.322 \\ + 0.54 & 0.492 & 0.776 \\ + 0.747 & 0.151 & 0.635 \\ + 0.02 & 0.13 & 0.306 \\ + 0.961 & 0.188 & 0.067 \\ + 0.336 & 0.751 & 0.065 \\ + 0.488 & 0.379 & 0.061 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $2.34$ +Volume: $0.24$ +Solid Angle: $0.86$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/32973.txt b/pretraining/mathematica/geometry/solids/32973.txt new file mode 100644 index 0000000000000000000000000000000000000000..3388751c7d41fd50a61e6b1a87a99d3eec50cad3 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/32973.txt @@ -0,0 +1,15 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.571 & 0.715 & 0.063 \\ + 0.182 & 0.396 & 0.168 \\ + 0.545 & 0.104 & 0.507 \\ + 0.009 & 0.117 & 0.614 \\ + 0.33 & 0.026 & 0.712 \\ + 0.034 & 0.051 & 0.047 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $0.27$ +Surface Area: $0.98$ +Volume: $0.05$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/37432.txt b/pretraining/mathematica/geometry/solids/37432.txt new file mode 100644 index 0000000000000000000000000000000000000000..ee99e96897089c1473c2cfac0c92596e492fd9de --- /dev/null +++ b/pretraining/mathematica/geometry/solids/37432.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.304 & 0.828 & 0.362 \\ + 0.576 & 0.787 & 0.994 \\ + 0.495 & 0.063 & 0.481 \\ + 0.176 & 0.243 & 0.929 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.04$ +Solid Angle: $0.37$ +Surface Area: $0.9$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/37615.txt b/pretraining/mathematica/geometry/solids/37615.txt new file mode 100644 index 0000000000000000000000000000000000000000..cf05142ba5a891993dd5749d5112c28a20b38182 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/37615.txt @@ -0,0 +1,15 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.086 & 0.631 & 0.237 \\ + 0.801 & 0.464 & 0.757 \\ + 0.844 & 0.981 & 0.078 \\ + 0.789 & 0.22 & 0.761 \\ + 0.089 & 0.114 & 0.781 \\ + 0.587 & 0.679 & 0.837 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.61$ +Solid Angle: $0.59$ +Volume: $0.09$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/41968.txt b/pretraining/mathematica/geometry/solids/41968.txt new file mode 100644 index 0000000000000000000000000000000000000000..cf8110e03a3112f31c8757c76b8aadf9732ed5f5 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/41968.txt @@ -0,0 +1,17 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.038 & 0.673 & 0.586 \\ + 0.888 & 0.969 & 0.577 \\ + 0.767 & 0.244 & 0.576 \\ + 0.872 & 0.556 & 0.135 \\ + 0.712 & 0.387 & 0.226 \\ + 0.893 & 0.995 & 0.719 \\ + 0.43 & 0.159 & 0.422 \\ + 0.159 & 0.537 & 0.777 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $1.09$ +Surface Area: $1.44$ +Volume: $0.11$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/43653.txt b/pretraining/mathematica/geometry/solids/43653.txt new file mode 100644 index 0000000000000000000000000000000000000000..ab02fe5db36daa01c8912298adf796e4241d72ff --- /dev/null +++ b/pretraining/mathematica/geometry/solids/43653.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.04 & 0.012 & 0.01 \\ + 0.964 & 0.416 & 0.505 \\ + 0.459 & 0.842 & 0.833 \\ + 0.988 & 0.81 & 0.621 \\ + 0.993 & 0.355 & 0.091 \\ + 0.889 & 0.354 & 0.292 \\ + 0.089 & 0.424 & 0.567 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $0.15$ +Volume: $0.07$ +Surface Area: $1.76$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/44053.txt b/pretraining/mathematica/geometry/solids/44053.txt new file mode 100644 index 0000000000000000000000000000000000000000..439340815723460dbd09ff39d4e88624dc652cae --- /dev/null +++ b/pretraining/mathematica/geometry/solids/44053.txt @@ -0,0 +1,17 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.941 & 0.117 & 0.787 \\ + 0.429 & 0.744 & 0.504 \\ + 0.948 & 0.235 & 0.461 \\ + 0.023 & 0.378 & 0.456 \\ + 0.317 & 0.514 & 0.117 \\ + 0.799 & 0.351 & 0.832 \\ + 0.16 & 0.342 & 0.801 \\ + 0.23 & 0.004 & 0.624 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.47$ +Volume: $0.12$ +Solid Angle: $1.13$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/48581.txt b/pretraining/mathematica/geometry/solids/48581.txt new file mode 100644 index 0000000000000000000000000000000000000000..f46a42d6b95a7941599645dadea4d805a2dae0dd --- /dev/null +++ b/pretraining/mathematica/geometry/solids/48581.txt @@ -0,0 +1,15 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + 0. & 0. & 1.192 \\ + 0.607 & 0. & 0.397 \\ + -0.304 & 0.526 & 0.397 \\ + 0.304 & 0.526 & -0.397 \\ + -0.304 & -0.526 & 0.397 \\ + 0.304 & -0.526 & -0.397 \\ + -0.607 & 0. & -0.397 \\ + 0. & 0. & -1.192 \\ +\end{array} +\right)$. Determine the Inradius. +Answer: +$0.43$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/50997.txt b/pretraining/mathematica/geometry/solids/50997.txt new file mode 100644 index 0000000000000000000000000000000000000000..8f61029af11d78173c18a3b754089d41cfd8c402 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/50997.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.912 & 0.994 & 0.491 \\ + 0.069 & 0.146 & 0.957 \\ + 0.344 & 0.895 & 0.339 \\ + 0.984 & 0.514 & 0.592 \\ + 0.256 & 0.785 & 0.692 \\ + 0.742 & 0.045 & 0.102 \\ + 0.809 & 0.12 & 0.521 \\ + 0.137 & 0.616 & 0.874 \\ + 0.508 & 0.95 & 0.863 \\ + 0.646 & 0.03 & 0.908 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $1.36$ +Surface Area: $2.47$ +Volume: $0.27$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/53434.txt b/pretraining/mathematica/geometry/solids/53434.txt new file mode 100644 index 0000000000000000000000000000000000000000..84036016715122e992b164c4ab2e872c8679da15 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/53434.txt @@ -0,0 +1,25 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + -\frac{i \left(1+(-1)^{2/9}\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{i \left(1+(-1)^{2/9}\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{i \left(1+(-1)^{2/9}\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{i \left(1+(-1)^{2/9}\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{(-1)^{11/18}}{(-1)^{2/9}-1} & 0 & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{(-1)^{11/18}}{2 \left((-1)^{2/9}-1\right)} & -\frac{(-1)^{11/18} \sqrt{3}}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{(-1)^{11/18}}{2 \left((-1)^{2/9}-1\right)} & \frac{(-1)^{11/18} \sqrt{3}}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{(-1)^{11/18}}{2 \left((-1)^{2/9}-1\right)} & -\frac{(-1)^{11/18} \sqrt{3}}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{(-1)^{11/18}}{2 \left((-1)^{2/9}-1\right)} & \frac{(-1)^{11/18} \sqrt{3}}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{(-1)^{11/18}}{(-1)^{2/9}-1} & 0 & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{(-1)^{7/18} \left(1+(-1)^{4/9}\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{(-1)^{8/9} \left((-1)^{4/9}-1\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{(-1)^{7/18} \left(1+(-1)^{4/9}\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{(-1)^{8/9} \left((-1)^{4/9}-1\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{(-1)^{7/18} \left(1+(-1)^{4/9}\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{(-1)^{8/9} \left((-1)^{4/9}-1\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{(-1)^{7/18} \left(1+(-1)^{4/9}\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{(-1)^{8/9} \left((-1)^{4/9}-1\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{\sqrt[18]{-1} \left(\sqrt[9]{-1}-1\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{(-1)^{5/9} \left(1+\sqrt[9]{-1}\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + -\frac{\sqrt[18]{-1} \left(\sqrt[9]{-1}-1\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{(-1)^{5/9} \left(1+\sqrt[9]{-1}\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{\sqrt[18]{-1} \left(\sqrt[9]{-1}-1\right)}{2 \left((-1)^{2/9}-1\right)} & -\frac{(-1)^{5/9} \left(1+\sqrt[9]{-1}\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ + \frac{\sqrt[18]{-1} \left(\sqrt[9]{-1}-1\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{(-1)^{5/9} \left(1+\sqrt[9]{-1}\right)}{2 \left((-1)^{2/9}-1\right)} & \frac{1}{2} \sqrt{1-\frac{\sqrt[9]{-1}}{\left(1+\sqrt[9]{-1}\right)^2}} \\ +\end{array} +\right)$. Determine the Volume. +Answer: +$\frac{1}{2} \sqrt{\frac{3}{2} \left(26+\frac{70}{\sqrt[3]{\frac{1}{2} \left(37+i \sqrt{3}\right)}}+5\ 2^{2/3} \sqrt[3]{37+i \sqrt{3}}\right)}$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/57106.txt b/pretraining/mathematica/geometry/solids/57106.txt new file mode 100644 index 0000000000000000000000000000000000000000..40add20fd956dffade7a1485e29aada371889b35 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/57106.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.061 & 0.172 & 0.495 \\ + 0.004 & 0.627 & 0.704 \\ + 0.109 & 0.478 & 0.287 \\ + 0.746 & 0.456 & 0.925 \\ + 0.931 & 0.647 & 0.074 \\ + 0.969 & 0.361 & 0.091 \\ + 0.717 & 0.885 & 0.525 \\ + 0.073 & 0.743 & 0.673 \\ + 0.158 & 0.743 & 0.614 \\ + 0.051 & 0.368 & 0.786 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.92$ +Volume: $0.18$ +Solid Angle: $1.65$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/57134.txt b/pretraining/mathematica/geometry/solids/57134.txt new file mode 100644 index 0000000000000000000000000000000000000000..0ae4b1c66e74bc58a7575be7c5a2b3247a20d154 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/57134.txt @@ -0,0 +1,5 @@ +Problem: +A sphere centered at $\{-3.149,-0.09,-3.843\}$ has radius $7.936$. Estimate the sphere's surface area and volume. +Answer: +Surface Area: $791.49$ +Volume: $2093.83$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/57137.txt b/pretraining/mathematica/geometry/solids/57137.txt new file mode 100644 index 0000000000000000000000000000000000000000..96259129a14bc01ed93c48ad9e9512355131703c --- /dev/null +++ b/pretraining/mathematica/geometry/solids/57137.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.613 & 0.108 & 0.046 \\ + 0.161 & 0.818 & 0.649 \\ + 0.811 & 0.845 & 0.927 \\ + 0.223 & 0.087 & 0.667 \\ + 0.564 & 0.737 & 0.313 \\ + 0.577 & 0.415 & 0.035 \\ + 0.137 & 0.222 & 0.455 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.59$ +Solid Angle: $0.81$ +Volume: $0.13$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/57142.txt b/pretraining/mathematica/geometry/solids/57142.txt new file mode 100644 index 0000000000000000000000000000000000000000..4d283b5450f4ef65fc8c78c9136cd3b4d4e47ff6 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/57142.txt @@ -0,0 +1,15 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.832 & 0.955 & 0.35 \\ + 0.133 & 0.246 & 0.075 \\ + 0.188 & 0.011 & 0.334 \\ + 0.035 & 0.98 & 0.352 \\ + 0.487 & 0.311 & 0.971 \\ + 0.662 & 0.789 & 0.575 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $0.65$ +Surface Area: $1.71$ +Volume: $0.12$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/58786.txt b/pretraining/mathematica/geometry/solids/58786.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d9c1eeeaadd9ae829a081fb59546b090835cd50 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/58786.txt @@ -0,0 +1,18 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.992 & 0.549 & 0.853 \\ + 0.303 & 0.435 & 0.005 \\ + 0.395 & 0.06 & 0.869 \\ + 0.94 & 0.228 & 0.535 \\ + 0.175 & 0.414 & 0.957 \\ + 0.852 & 0.686 & 0.31 \\ + 0.556 & 0.922 & 0.886 \\ + 0.775 & 0.021 & 0.498 \\ + 0.011 & 0.695 & 0.654 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $2.29$ +Solid Angle: $1.86$ +Volume: $0.25$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/59056.txt b/pretraining/mathematica/geometry/solids/59056.txt new file mode 100644 index 0000000000000000000000000000000000000000..0ff2f1eef51c683520bdf64fde37af9c4e13f764 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/59056.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.277 & 0.754 & 0.27 \\ + 0.774 & 0.296 & 0.878 \\ + 0.868 & 0.891 & 0.796 \\ + 0.748 & 0.646 & 0.954 \\ + 0.919 & 0.625 & 0.743 \\ + 0.568 & 0.285 & 0.578 \\ + 0.028 & 0.476 & 0.997 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.31$ +Solid Angle: $0.64$ +Volume: $0.09$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/65769.txt b/pretraining/mathematica/geometry/solids/65769.txt new file mode 100644 index 0000000000000000000000000000000000000000..17d5fb518bc6e3e91b95ecbc0bba2e63a2abfcbd --- /dev/null +++ b/pretraining/mathematica/geometry/solids/65769.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.494 & 0.566 & 0.021 \\ + 0.8 & 0.263 & 0.772 \\ + 0.27 & 0.27 & 0.897 \\ + 0.427 & 0.992 & 0.901 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.05$ +Surface Area: $1.1$ +Solid Angle: $0.25$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/68795.txt b/pretraining/mathematica/geometry/solids/68795.txt new file mode 100644 index 0000000000000000000000000000000000000000..b64bb4b36b9c1e2f58ad87f1e41602125b88a8b3 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/68795.txt @@ -0,0 +1,21 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + -1.038 & -0.5 & 0.429 \\ + -1.038 & 0.5 & 0.429 \\ + 1.038 & -0.5 & -0.429 \\ + 1.038 & 0.5 & -0.429 \\ + -1.152 & 0. & -0.429 \\ + 1.152 & 0. & 0.429 \\ + -0.256 & -1.123 & 0.429 \\ + -0.256 & 1.123 & 0.429 \\ + 0.256 & -1.123 & -0.429 \\ + 0.256 & 1.123 & -0.429 \\ + -0.718 & -0.901 & -0.429 \\ + -0.718 & 0.901 & -0.429 \\ + 0.718 & -0.901 & 0.429 \\ + 0.718 & 0.901 & 0.429 \\ +\end{array} +\right)$. Determine the Circumradius. +Answer: +$1.23$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/69430.txt b/pretraining/mathematica/geometry/solids/69430.txt new file mode 100644 index 0000000000000000000000000000000000000000..256ea2038c4cc0f44376a0aa23480f1ee2db9454 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/69430.txt @@ -0,0 +1,57 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + -1.633 & -0.816 & -0.577 \\ + -1.633 & -0.816 & 0.577 \\ + -1.633 & 0. & 0. \\ + -1.633 & 0.816 & -0.577 \\ + -1.633 & 0.816 & 0.577 \\ + -0.816 & -1.633 & -0.577 \\ + -0.816 & -1.633 & 0.577 \\ + -0.816 & -0.816 & -1.155 \\ + -0.816 & -0.816 & 0. \\ + -0.816 & -0.816 & 1.155 \\ + -0.816 & 0. & -1.732 \\ + -0.816 & 0. & -0.577 \\ + -0.816 & 0. & 0.577 \\ + -0.816 & 0. & 1.732 \\ + -0.816 & 0.816 & -1.155 \\ + -0.816 & 0.816 & 0. \\ + -0.816 & 0.816 & 1.155 \\ + -0.816 & 1.633 & -0.577 \\ + -0.816 & 1.633 & 0.577 \\ + 0. & -1.633 & 0. \\ + 0. & -0.816 & -1.732 \\ + 0. & -0.816 & -0.577 \\ + 0. & -0.816 & 0.577 \\ + 0. & -0.816 & 1.732 \\ + 0. & 0. & -1.155 \\ + 0. & 0. & 1.155 \\ + 0. & 0.816 & -1.732 \\ + 0. & 0.816 & -0.577 \\ + 0. & 0.816 & 0.577 \\ + 0. & 0.816 & 1.732 \\ + 0. & 1.633 & 0. \\ + 0.816 & -1.633 & -0.577 \\ + 0.816 & -1.633 & 0.577 \\ + 0.816 & -0.816 & -1.155 \\ + 0.816 & -0.816 & 0. \\ + 0.816 & -0.816 & 1.155 \\ + 0.816 & 0. & -1.732 \\ + 0.816 & 0. & -0.577 \\ + 0.816 & 0. & 0.577 \\ + 0.816 & 0. & 1.732 \\ + 0.816 & 0.816 & -1.155 \\ + 0.816 & 0.816 & 0. \\ + 0.816 & 0.816 & 1.155 \\ + 0.816 & 1.633 & -0.577 \\ + 0.816 & 1.633 & 0.577 \\ + 1.633 & -0.816 & -0.577 \\ + 1.633 & -0.816 & 0.577 \\ + 1.633 & 0. & 0. \\ + 1.633 & 0.816 & -0.577 \\ + 1.633 & 0.816 & 0.577 \\ +\end{array} +\right)$. Determine the EdgeCount. +Answer: +$120.$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/70413.txt b/pretraining/mathematica/geometry/solids/70413.txt new file mode 100644 index 0000000000000000000000000000000000000000..1c68aaafae6ac9ed87fd06fcd565e0b101e3bc0e --- /dev/null +++ b/pretraining/mathematica/geometry/solids/70413.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.942 & 0.026 & 0.867 \\ + 0.738 & 0.574 & 0.044 \\ + 0.125 & 0.568 & 0.203 \\ + 0.753 & 0.57 & 0.282 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $0.04$ +Surface Area: $0.71$ +Volume: $0.01$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/70513.txt b/pretraining/mathematica/geometry/solids/70513.txt new file mode 100644 index 0000000000000000000000000000000000000000..dff563d6fff1cc2324bb6cf33e6b54a48ab59344 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/70513.txt @@ -0,0 +1,14 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.111 & 0.004 & 0.158 \\ + 0.454 & 0.242 & 0.176 \\ + 0.235 & 0.594 & 0.295 \\ + 0.341 & 0.625 & 0.742 \\ + 0.056 & 0.838 & 0.564 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $0.68$ +Solid Angle: $0.29$ +Volume: $0.03$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/71243.txt b/pretraining/mathematica/geometry/solids/71243.txt new file mode 100644 index 0000000000000000000000000000000000000000..459b440c10fa2ce5bec3261a2befe4b08d69a604 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/71243.txt @@ -0,0 +1,18 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.317 & 0.77 & 0.519 \\ + 0.954 & 0.014 & 0.867 \\ + 0.551 & 0.345 & 0.217 \\ + 0.947 & 0.463 & 0.624 \\ + 0.126 & 0.012 & 0.635 \\ + 0.824 & 0.484 & 0.82 \\ + 0.579 & 0.736 & 0.666 \\ + 0.596 & 0.744 & 0.219 \\ + 0.308 & 0.199 & 0.734 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.12$ +Surface Area: $1.55$ +Solid Angle: $1.6$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/71837.txt b/pretraining/mathematica/geometry/solids/71837.txt new file mode 100644 index 0000000000000000000000000000000000000000..40b032cd87ac55f3dcdfb3c0d7b9d29498ded0aa --- /dev/null +++ b/pretraining/mathematica/geometry/solids/71837.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.064 & 0.687 & 0.305 \\ + 0.684 & 0.916 & 0.827 \\ + 0.449 & 0.688 & 0.866 \\ + 0.321 & 0.887 & 0.317 \\ + 0.259 & 0.176 & 0.756 \\ + 0.084 & 0.007 & 0.508 \\ + 0.735 & 0.705 & 0.715 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.05$ +Surface Area: $1.15$ +Solid Angle: $0.86$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/73105.txt b/pretraining/mathematica/geometry/solids/73105.txt new file mode 100644 index 0000000000000000000000000000000000000000..5453e7b72b3e3343ae5f85de3591776de3f93214 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/73105.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.979 & 0.234 & 0.099 \\ + 0.303 & 0.643 & 0.636 \\ + 0.788 & 0.873 & 0.467 \\ + 0.918 & 0.59 & 0.627 \\ + 0.275 & 0.084 & 0.612 \\ + 0.459 & 0.819 & 0.103 \\ + 0.766 & 0.187 & 0.959 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.75$ +Volume: $0.16$ +Solid Angle: $0.97$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/73142.txt b/pretraining/mathematica/geometry/solids/73142.txt new file mode 100644 index 0000000000000000000000000000000000000000..869dd3be873802944ee11b2ecbab7d2a70247264 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/73142.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.91 & 0.117 & 0.666 \\ + 0.288 & 0.147 & 0.333 \\ + 0.489 & 0.115 & 0.256 \\ + 0.872 & 0.929 & 0.775 \\ + 0.809 & 0.478 & 0.902 \\ + 0.157 & 0.581 & 0.187 \\ + 0.208 & 0.778 & 0.597 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.52$ +Volume: $0.1$ +Solid Angle: $0.75$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/73287.txt b/pretraining/mathematica/geometry/solids/73287.txt new file mode 100644 index 0000000000000000000000000000000000000000..8214c2c89b5c018fa78a454e56b8af63ed89cfd0 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/73287.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.49 & 0.06 & 0.369 \\ + 0.263 & 0.548 & 0.127 \\ + 0.912 & 0.984 & 0. \\ + 0.923 & 0.857 & 0.141 \\ + 0.484 & 0.659 & 0.996 \\ + 0.914 & 0.686 & 0.435 \\ + 0.749 & 0.556 & 0.19 \\ + 0.042 & 0.079 & 0.421 \\ + 0.496 & 0.622 & 0.11 \\ + 0.433 & 0.114 & 0.886 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.17$ +Solid Angle: $2.48$ +Surface Area: $1.97$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/74382.txt b/pretraining/mathematica/geometry/solids/74382.txt new file mode 100644 index 0000000000000000000000000000000000000000..123a3f033b7aa88226ae6960e930b608e56e6d6f --- /dev/null +++ b/pretraining/mathematica/geometry/solids/74382.txt @@ -0,0 +1,18 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.095 & 0.477 & 0.138 \\ + 0.346 & 0.56 & 0.881 \\ + 0.964 & 0.402 & 0.465 \\ + 0.542 & 0.091 & 0.022 \\ + 0.087 & 0.316 & 0.413 \\ + 0.018 & 0.431 & 0.501 \\ + 0.877 & 0.432 & 0.475 \\ + 0.192 & 0.674 & 0.958 \\ + 0.778 & 0.216 & 0.501 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.08$ +Solid Angle: $1.24$ +Surface Area: $1.39$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/74469.txt b/pretraining/mathematica/geometry/solids/74469.txt new file mode 100644 index 0000000000000000000000000000000000000000..141ae3189a61d7ceb95d9767dcf02b0e78ae5ec4 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/74469.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.791 & 0.203 & 0.029 \\ + 0.926 & 0.592 & 0.058 \\ + 0.566 & 0.103 & 0.057 \\ + 0.319 & 0.002 & 0.535 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.01$ +Surface Area: $0.38$ +Solid Angle: $1.15$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/75003.txt b/pretraining/mathematica/geometry/solids/75003.txt new file mode 100644 index 0000000000000000000000000000000000000000..b05ad75e313757d0e298b7cbbe83ba0788746afa --- /dev/null +++ b/pretraining/mathematica/geometry/solids/75003.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.552 & 0.376 & 0.73 \\ + 0.167 & 0.133 & 0.826 \\ + 0.572 & 0.97 & 0.612 \\ + 0.046 & 0.991 & 0.733 \\ + 0.168 & 0.309 & 0.174 \\ + 0.913 & 0.481 & 0.336 \\ + 0.749 & 0.845 & 0.286 \\ + 0.827 & 0.679 & 0.243 \\ + 0.888 & 0.948 & 0.713 \\ + 0.387 & 0.178 & 0.495 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.2$ +Solid Angle: $4.31$ +Surface Area: $2.$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/75734.txt b/pretraining/mathematica/geometry/solids/75734.txt new file mode 100644 index 0000000000000000000000000000000000000000..e2303bcef6472fce70a2fe2639783da025248171 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/75734.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.839 & 0.925 & 0.621 \\ + 0.248 & 0.129 & 0.801 \\ + 0.791 & 0.001 & 0.018 \\ + 0.071 & 0.993 & 0.672 \\ + 0.874 & 0.949 & 0.556 \\ + 0.015 & 0.945 & 0.834 \\ + 0.014 & 0.964 & 0.465 \\ + 0.979 & 0.582 & 0.909 \\ + 0.76 & 0.962 & 0.228 \\ + 0.031 & 0.334 & 0.436 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.35$ +Solid Angle: $4.99$ +Surface Area: $2.89$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/76014.txt b/pretraining/mathematica/geometry/solids/76014.txt new file mode 100644 index 0000000000000000000000000000000000000000..362f844c0254fb186acc06147387d18c5e5e4a01 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/76014.txt @@ -0,0 +1,17 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.762 & 0.291 & 0.665 \\ + 0.578 & 0.648 & 0.356 \\ + 0.775 & 0.654 & 0.858 \\ + 0.201 & 0.757 & 0.727 \\ + 0.469 & 0.333 & 0.205 \\ + 0.298 & 0.802 & 0.722 \\ + 0.18 & 0.804 & 0.691 \\ + 0.84 & 0.369 & 0.283 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.05$ +Surface Area: $0.91$ +Solid Angle: $1.66$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/76655.txt b/pretraining/mathematica/geometry/solids/76655.txt new file mode 100644 index 0000000000000000000000000000000000000000..8cef659022c1217491d32d30c669779daf63bba1 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/76655.txt @@ -0,0 +1,18 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.28 & 0.16 & 0.919 \\ + 0.912 & 0.033 & 0.392 \\ + 0.146 & 0.302 & 0.192 \\ + 0.716 & 0.1 & 0.709 \\ + 0.35 & 0.031 & 0.292 \\ + 0.384 & 0.718 & 0.392 \\ + 0.725 & 0.902 & 0.997 \\ + 0.176 & 0.731 & 0.253 \\ + 0.591 & 0.372 & 0.878 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.17$ +Solid Angle: $1.53$ +Surface Area: $1.91$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/78192.txt b/pretraining/mathematica/geometry/solids/78192.txt new file mode 100644 index 0000000000000000000000000000000000000000..a9ddd4501467d77d0b74480b2ec2f03aab1160f8 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/78192.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.606 & 0.671 & 0.39 \\ + 0.592 & 0.311 & 0.291 \\ + 0.046 & 0.963 & 0.56 \\ + 0.898 & 0.643 & 0.076 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $3.29$ +Surface Area: $0.49$ +Volume: $0.01$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/7832.txt b/pretraining/mathematica/geometry/solids/7832.txt new file mode 100644 index 0000000000000000000000000000000000000000..839165c5ef56896174356c458147a6d38013cd5c --- /dev/null +++ b/pretraining/mathematica/geometry/solids/7832.txt @@ -0,0 +1,25 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + -\frac{1}{\sqrt{2}} & 0 & 0 \\ + -\frac{1}{2} & -\frac{1}{2} & 0 \\ + -\frac{1}{2} & 0 & -\frac{1}{2} \\ + -\frac{1}{2} & 0 & \frac{1}{2} \\ + -\frac{1}{2} & \frac{1}{2} & 0 \\ + 0 & -\frac{1}{\sqrt{2}} & 0 \\ + 0 & -\frac{1}{2} & -\frac{1}{2} \\ + 0 & -\frac{1}{2} & \frac{1}{2} \\ + 0 & 0 & -\frac{1}{\sqrt{2}} \\ + 0 & 0 & \frac{1}{\sqrt{2}} \\ + 0 & \frac{1}{2} & -\frac{1}{2} \\ + 0 & \frac{1}{2} & \frac{1}{2} \\ + 0 & \frac{1}{\sqrt{2}} & 0 \\ + \frac{1}{2} & -\frac{1}{2} & 0 \\ + \frac{1}{2} & 0 & -\frac{1}{2} \\ + \frac{1}{2} & 0 & \frac{1}{2} \\ + \frac{1}{2} & \frac{1}{2} & 0 \\ + \frac{1}{\sqrt{2}} & 0 & 0 \\ +\end{array} +\right)$. Determine the FaceCount. +Answer: +$32$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/80394.txt b/pretraining/mathematica/geometry/solids/80394.txt new file mode 100644 index 0000000000000000000000000000000000000000..74ce39389dad907c4205da00f340e319257c6da1 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/80394.txt @@ -0,0 +1,21 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + -\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{6}} & -\frac{1}{2 \sqrt{3}} \\ + -\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{6}} & \frac{1}{2 \sqrt{3}} \\ + -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} & -\frac{1}{2 \sqrt{3}} \\ + -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} & \frac{1}{2 \sqrt{3}} \\ + 0 & -\sqrt{\frac{2}{3}} & -\frac{1}{2 \sqrt{3}} \\ + 0 & -\sqrt{\frac{2}{3}} & \frac{1}{2 \sqrt{3}} \\ + 0 & 0 & -\frac{\sqrt{3}}{2} \\ + 0 & 0 & \frac{\sqrt{3}}{2} \\ + 0 & \sqrt{\frac{2}{3}} & -\frac{1}{2 \sqrt{3}} \\ + 0 & \sqrt{\frac{2}{3}} & \frac{1}{2 \sqrt{3}} \\ + \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{6}} & -\frac{1}{2 \sqrt{3}} \\ + \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{6}} & \frac{1}{2 \sqrt{3}} \\ + \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} & -\frac{1}{2 \sqrt{3}} \\ + \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} & \frac{1}{2 \sqrt{3}} \\ +\end{array} +\right)$. Determine the Circumdiameter. +Answer: +$\sqrt{3}$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/81682.txt b/pretraining/mathematica/geometry/solids/81682.txt new file mode 100644 index 0000000000000000000000000000000000000000..3d47dd921fafd9bd30a10e7bf192f3d69996fa98 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/81682.txt @@ -0,0 +1,18 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.899 & 0.037 & 0.663 \\ + 0.773 & 0.709 & 0.477 \\ + 0.178 & 0.977 & 0.228 \\ + 0.759 & 0.309 & 0.174 \\ + 0.661 & 0.238 & 0.89 \\ + 0.645 & 0.971 & 0.14 \\ + 0.455 & 0.41 & 0.903 \\ + 0.724 & 0.991 & 0.663 \\ + 0.256 & 0.05 & 0.756 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $2.06$ +Solid Angle: $1.28$ +Volume: $0.2$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/86218.txt b/pretraining/mathematica/geometry/solids/86218.txt new file mode 100644 index 0000000000000000000000000000000000000000..52018dc4adb86dee2d547f4aeaae17c4a782e5c1 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/86218.txt @@ -0,0 +1,13 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.859 & 0.301 & 0.157 \\ + 0.915 & 0.918 & 0.627 \\ + 0.112 & 0.015 & 0.918 \\ + 0.488 & 0.859 & 0.969 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Volume: $0.01$ +Surface Area: $1.32$ +Solid Angle: $0.07$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/8741.txt b/pretraining/mathematica/geometry/solids/8741.txt new file mode 100644 index 0000000000000000000000000000000000000000..f7391d099b0c8ac340bb9ffadee3a3c7aa521795 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/8741.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.566 & 0.275 & 0.434 \\ + 0.196 & 0.768 & 0.425 \\ + 0.341 & 0.298 & 0.528 \\ + 0.068 & 0.48 & 0.74 \\ + 0.99 & 0.846 & 0.339 \\ + 0.206 & 0.838 & 0.642 \\ + 0.239 & 0.782 & 0.905 \\ + 0.603 & 0.449 & 0.033 \\ + 0.372 & 0.763 & 0.909 \\ + 0.438 & 0.359 & 0.693 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.41$ +Solid Angle: $2.69$ +Volume: $0.11$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/88270.txt b/pretraining/mathematica/geometry/solids/88270.txt new file mode 100644 index 0000000000000000000000000000000000000000..09fd17021c8d6ca027e6983b7da8a3e0f1c2eb3b --- /dev/null +++ b/pretraining/mathematica/geometry/solids/88270.txt @@ -0,0 +1,16 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.825 & 0.203 & 0.744 \\ + 0.622 & 0.052 & 0.289 \\ + 0.086 & 0.648 & 0.082 \\ + 0.112 & 0.011 & 0.289 \\ + 0.552 & 0.714 & 0.487 \\ + 0.944 & 0.697 & 0.978 \\ + 0.321 & 0.307 & 0.896 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $2.07$ +Surface Area: $1.78$ +Volume: $0.14$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/90183.txt b/pretraining/mathematica/geometry/solids/90183.txt new file mode 100644 index 0000000000000000000000000000000000000000..6dca7861ec15c8c1e09800cbcb5c2a7efe2b8e1c --- /dev/null +++ b/pretraining/mathematica/geometry/solids/90183.txt @@ -0,0 +1,27 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + 0.309 & -0.5 & 0. \\ + 0.809 & -0.809 & 0.809 \\ + 0.5 & 0. & 0.309 \\ + 0.809 & 0.809 & 0.809 \\ + 0.309 & 0.5 & 0. \\ + 0.809 & -0.809 & -0.809 \\ + 0.5 & 0. & -0.309 \\ + 0.809 & 0.809 & -0.809 \\ + -0.309 & -0.5 & 0. \\ + -0.809 & -0.809 & 0.809 \\ + -0.5 & 0. & 0.309 \\ + -0.809 & 0.809 & 0.809 \\ + -0.309 & 0.5 & 0. \\ + -0.809 & -0.809 & -0.809 \\ + -0.5 & 0. & -0.309 \\ + -0.809 & 0.809 & -0.809 \\ + 0. & 0.309 & -0.5 \\ + 0. & 0.309 & 0.5 \\ + 0. & -0.309 & -0.5 \\ + 0. & -0.309 & 0.5 \\ +\end{array} +\right)$. Determine the SurfaceArea. +Answer: +$9.23$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/94462.txt b/pretraining/mathematica/geometry/solids/94462.txt new file mode 100644 index 0000000000000000000000000000000000000000..c6a10bfc9021d7b3284edb217641918f477cadb8 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/94462.txt @@ -0,0 +1,20 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.38 & 0.423 & 0.366 \\ + 0.421 & 0.174 & 0.391 \\ + 0.293 & 0.403 & 0.988 \\ + 0.751 & 0.642 & 0.831 \\ + 0.454 & 0.156 & 0.848 \\ + 0.989 & 0.997 & 0.161 \\ + 0.849 & 0.594 & 0.649 \\ + 0.981 & 0.363 & 0.072 \\ + 0.646 & 0.896 & 0.073 \\ + 0.805 & 0.144 & 0.65 \\ + 0.572 & 0.143 & 0.54 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $1.86$ +Solid Angle: $3.84$ +Volume: $0.17$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/95209.txt b/pretraining/mathematica/geometry/solids/95209.txt new file mode 100644 index 0000000000000000000000000000000000000000..9b09792590fb3781a1b2a68725cd685d7721b8e8 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/95209.txt @@ -0,0 +1,19 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.261 & 0.404 & 0.25 \\ + 0.916 & 0.094 & 0.804 \\ + 0.044 & 0.474 & 0.962 \\ + 0.033 & 0.033 & 0.366 \\ + 0.882 & 0.312 & 0.214 \\ + 0.01 & 0.66 & 0.3 \\ + 0.813 & 0.781 & 0.871 \\ + 0.207 & 0.143 & 0.246 \\ + 0.814 & 0.971 & 0.815 \\ + 0.371 & 0.915 & 0.493 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Surface Area: $2.55$ +Solid Angle: $5.89$ +Volume: $0.3$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/9567.txt b/pretraining/mathematica/geometry/solids/9567.txt new file mode 100644 index 0000000000000000000000000000000000000000..a1f3ac7193cd68a88c876b2b28f9f69011dd507c --- /dev/null +++ b/pretraining/mathematica/geometry/solids/9567.txt @@ -0,0 +1,67 @@ +Problem: +A polyhedron has vertex coordinates $\left( +\begin{array}{ccc} + -\frac{1}{2}-\frac{1}{\sqrt{5}} & -\frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & -\frac{1}{2 \sqrt{5}} \\ + -\frac{1}{2}-\frac{1}{\sqrt{5}} & \sqrt{\frac{1}{4}-\frac{1}{2 \sqrt{5}}} & -\frac{1}{2 \sqrt{5}} \\ + -\frac{3}{4}-\frac{1}{4 \sqrt{5}} & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{2 \sqrt{5}} \\ + -\frac{3}{4}-\frac{1}{4 \sqrt{5}} & \sqrt{\frac{1}{8}+\frac{1}{8 \sqrt{5}}} & \frac{1}{2 \sqrt{5}} \\ + \frac{1}{4} \left(-1-\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & -\frac{1}{2} \\ + \frac{1}{4} \left(-1-\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{2} \\ + \frac{1}{4} \left(-1-\sqrt{5}\right) & \sqrt{\frac{1}{8}-\frac{1}{8 \sqrt{5}}} & -\frac{1}{2} \\ + \frac{1}{4} \left(-1-\sqrt{5}\right) & \sqrt{\frac{1}{8}-\frac{1}{8 \sqrt{5}}} & \frac{1}{2} \\ + \frac{1}{10} \left(-5-\sqrt{5}\right) & 0 & -\frac{3}{2 \sqrt{5}} \\ + -\frac{3}{2 \sqrt{5}} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{2 \sqrt{5}} \\ + -\frac{3}{2 \sqrt{5}} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & \frac{1}{2 \sqrt{5}} \\ + \frac{1}{20} \left(-5-3 \sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{3}{2 \sqrt{5}} \\ + \frac{1}{20} \left(-5-3 \sqrt{5}\right) & \sqrt{\frac{1}{8}+\frac{1}{8 \sqrt{5}}} & \frac{3}{2 \sqrt{5}} \\ + -\frac{1}{2} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & -\frac{1}{2} \\ + -\frac{1}{2} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{2} \\ + -\frac{1}{2} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & -\frac{1}{2} \\ + -\frac{1}{2} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & \frac{1}{2} \\ + -\frac{1}{\sqrt{5}} & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & -\frac{1}{2 \sqrt{5}} \\ + -\frac{1}{\sqrt{5}} & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & -\frac{1}{2 \sqrt{5}} \\ + \frac{1}{10} \left(\sqrt{5}-5\right) & 0 & -\frac{1}{2}-\frac{1}{\sqrt{5}} \\ + -\frac{1}{2 \sqrt{5}} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & -\frac{3}{2 \sqrt{5}} \\ + -\frac{1}{2 \sqrt{5}} & -\frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & \frac{1}{2}+\frac{1}{\sqrt{5}} \\ + -\frac{1}{2 \sqrt{5}} & \sqrt{\frac{1}{4}-\frac{1}{2 \sqrt{5}}} & \frac{1}{2}+\frac{1}{\sqrt{5}} \\ + -\frac{1}{2 \sqrt{5}} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & -\frac{3}{2 \sqrt{5}} \\ + \frac{1}{20} \left(\sqrt{5}-5\right) & -\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & -\frac{1}{2 \sqrt{5}} \\ + \frac{1}{20} \left(\sqrt{5}-5\right) & \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} & -\frac{1}{2 \sqrt{5}} \\ + \frac{1}{20} \left(5-3 \sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & -\frac{1}{2}-\frac{1}{\sqrt{5}} \\ + \frac{1}{20} \left(5-3 \sqrt{5}\right) & \sqrt{\frac{1}{8}-\frac{1}{8 \sqrt{5}}} & -\frac{1}{2}-\frac{1}{\sqrt{5}} \\ + 0 & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & -\frac{1}{2} \\ + 0 & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{2} \\ + 0 & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & -\frac{1}{2} \\ + 0 & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{2} \\ + \frac{1}{20} \left(3 \sqrt{5}-5\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{2}+\frac{1}{\sqrt{5}} \\ + \frac{1}{20} \left(3 \sqrt{5}-5\right) & \sqrt{\frac{1}{8}-\frac{1}{8 \sqrt{5}}} & \frac{1}{2}+\frac{1}{\sqrt{5}} \\ + \frac{1}{20} \left(5-\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} & \frac{1}{2 \sqrt{5}} \\ + \frac{1}{20} \left(5-\sqrt{5}\right) & \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}} & \frac{1}{2 \sqrt{5}} \\ + \frac{1}{2 \sqrt{5}} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{3}{2 \sqrt{5}} \\ + \frac{1}{2 \sqrt{5}} & -\frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & -\frac{1}{2}-\frac{1}{\sqrt{5}} \\ + \frac{1}{2 \sqrt{5}} & \sqrt{\frac{1}{4}-\frac{1}{2 \sqrt{5}}} & -\frac{1}{2}-\frac{1}{\sqrt{5}} \\ + \frac{1}{2 \sqrt{5}} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & \frac{3}{2 \sqrt{5}} \\ + \frac{1}{10} \left(5-\sqrt{5}\right) & 0 & \frac{1}{2}+\frac{1}{\sqrt{5}} \\ + \frac{1}{\sqrt{5}} & -\sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{2 \sqrt{5}} \\ + \frac{1}{\sqrt{5}} & \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & \frac{1}{2 \sqrt{5}} \\ + \frac{1}{2} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & -\frac{1}{2} \\ + \frac{1}{2} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & \frac{1}{2} \\ + \frac{1}{2} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & -\frac{1}{2} \\ + \frac{1}{2} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & \frac{1}{2} \\ + \frac{1}{20} \left(5+3 \sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & -\frac{3}{2 \sqrt{5}} \\ + \frac{1}{20} \left(5+3 \sqrt{5}\right) & \sqrt{\frac{1}{8}+\frac{1}{8 \sqrt{5}}} & -\frac{3}{2 \sqrt{5}} \\ + \frac{3}{2 \sqrt{5}} & -\frac{1}{2} \sqrt{1+\frac{2}{\sqrt{5}}} & -\frac{1}{2 \sqrt{5}} \\ + \frac{3}{2 \sqrt{5}} & \sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & -\frac{1}{2 \sqrt{5}} \\ + \frac{1}{10} \left(5+\sqrt{5}\right) & 0 & \frac{3}{2 \sqrt{5}} \\ + \frac{1}{4} \left(1+\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & -\frac{1}{2} \\ + \frac{1}{4} \left(1+\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{2} \\ + \frac{1}{4} \left(1+\sqrt{5}\right) & \sqrt{\frac{1}{8}-\frac{1}{8 \sqrt{5}}} & -\frac{1}{2} \\ + \frac{1}{4} \left(1+\sqrt{5}\right) & \sqrt{\frac{1}{8}-\frac{1}{8 \sqrt{5}}} & \frac{1}{2} \\ + \frac{1}{20} \left(15+\sqrt{5}\right) & -\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & -\frac{1}{2 \sqrt{5}} \\ + \frac{1}{20} \left(15+\sqrt{5}\right) & \sqrt{\frac{1}{8}+\frac{1}{8 \sqrt{5}}} & -\frac{1}{2 \sqrt{5}} \\ + \frac{1}{2}+\frac{1}{\sqrt{5}} & -\frac{1}{2} \sqrt{1-\frac{2}{\sqrt{5}}} & \frac{1}{2 \sqrt{5}} \\ + \frac{1}{2}+\frac{1}{\sqrt{5}} & \sqrt{\frac{1}{4}-\frac{1}{2 \sqrt{5}}} & \frac{1}{2 \sqrt{5}} \\ +\end{array} +\right)$. Determine the GeneralizedDiameter. +Answer: +$\sqrt{3+\frac{2}{\sqrt{5}}}$ \ No newline at end of file diff --git a/pretraining/mathematica/geometry/solids/96476.txt b/pretraining/mathematica/geometry/solids/96476.txt new file mode 100644 index 0000000000000000000000000000000000000000..7b976a2076d6709930e100533cc6faed373065b5 --- /dev/null +++ b/pretraining/mathematica/geometry/solids/96476.txt @@ -0,0 +1,17 @@ +Problem: +A polyhedron has vertices with the coordinates $\left( +\begin{array}{ccc} + 0.85 & 0.304 & 0.958 \\ + 0.876 & 0.887 & 0.699 \\ + 0.733 & 0.192 & 0.884 \\ + 0.082 & 0.728 & 0.643 \\ + 0.999 & 0.216 & 0.016 \\ + 0.626 & 0.745 & 0.999 \\ + 0.673 & 0.729 & 0.195 \\ + 0.777 & 0.293 & 0.204 \\ +\end{array} +\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. +Answer: +Solid Angle: $2.04$ +Volume: $0.16$ +Surface Area: $1.81$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/10592.txt b/pretraining/mathematica/number_theory/relatively_prime/10592.txt new file mode 100644 index 0000000000000000000000000000000000000000..fa3f408f8b679e150729f07cc73de0eb22991015 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/10592.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{-73,973,507\}$. +Answer: +$\text{True}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/1480.txt b/pretraining/mathematica/number_theory/relatively_prime/1480.txt new file mode 100644 index 0000000000000000000000000000000000000000..ab0b79529f06e480898a2674b5b6276b0357cc07 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/1480.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{520,362,61\}$. +Answer: +$\text{False}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/3188.txt b/pretraining/mathematica/number_theory/relatively_prime/3188.txt new file mode 100644 index 0000000000000000000000000000000000000000..f8d330ba4507741ba7ccd90404d7289be64403b3 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/3188.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{5,-996,899\}$. +Answer: +$\text{True}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/33549.txt b/pretraining/mathematica/number_theory/relatively_prime/33549.txt new file mode 100644 index 0000000000000000000000000000000000000000..ab7612fca5c73b39de7d79fe0e2b73bf07ee1639 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/33549.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{-54,9,10\}$. +Answer: +$\text{False}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/34044.txt b/pretraining/mathematica/number_theory/relatively_prime/34044.txt new file mode 100644 index 0000000000000000000000000000000000000000..f026e867703cfc781b1f3159940cb953ebb17271 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/34044.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{-75,398\}$. +Answer: +$\text{True}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/36034.txt b/pretraining/mathematica/number_theory/relatively_prime/36034.txt new file mode 100644 index 0000000000000000000000000000000000000000..796400c53f39394b1fefc02b0989612f873503e8 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/36034.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{-673,210,-16\}$. +Answer: +$\text{False}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/39671.txt b/pretraining/mathematica/number_theory/relatively_prime/39671.txt new file mode 100644 index 0000000000000000000000000000000000000000..d901170f6254d7ead5049da004bbc1f808e90830 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/39671.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{442,114,699\}$. +Answer: +$\text{False}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/43933.txt b/pretraining/mathematica/number_theory/relatively_prime/43933.txt new file mode 100644 index 0000000000000000000000000000000000000000..68f6017007c5751c722b581a133e93ef6eeec7d0 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/43933.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{3,-79,-395\}$. +Answer: +$\text{False}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/48146.txt b/pretraining/mathematica/number_theory/relatively_prime/48146.txt new file mode 100644 index 0000000000000000000000000000000000000000..40b361d508acf92b588c1803ac89880e0f8219e7 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/48146.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{-753,-382\}$. +Answer: +$\text{True}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/7889.txt b/pretraining/mathematica/number_theory/relatively_prime/7889.txt new file mode 100644 index 0000000000000000000000000000000000000000..5607e2beece59704ff52d1b449870a4a0d4c92cf --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/7889.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{-951,886\}$. +Answer: +$\text{True}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/relatively_prime/9201.txt b/pretraining/mathematica/number_theory/relatively_prime/9201.txt new file mode 100644 index 0000000000000000000000000000000000000000..36804eb77bd34305a6427cbf276597957b0880f3 --- /dev/null +++ b/pretraining/mathematica/number_theory/relatively_prime/9201.txt @@ -0,0 +1,4 @@ +Problem: +Are the following numbers relatively prime (coprime)? $\{155,-272,-63\}$. +Answer: +$\text{True}$ \ No newline at end of file