messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 3
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.111 & 0.452 \\\\\n 0.2 & 0.965 \\\\\n 0.276 & 0.855 \\\\\n 0.338 & 0.393 \\\\\n 0.4 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.233 & 0.171 \\\\\n 0.636 & 0.413 \\\\\n 0.924 & 0.302 \\\\\n\\end{arra... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.625 & 0.939 \\\\\n -0.605 & 0.725 \\\\\n -0.418 & 0.363 \\\\\n -0.393 & 0.818 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.542 & 0.427 \\\\\n -0.536 & 0.593 \\\\\n -0.395 & 0.646 \\\\\n -0.18 & 0.083 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.132 & 0.674 \\\\\n 0.293 & 0.949 \\\\\n 0.293 & 0.53 \\\\\n 0.365 & 0.961 \\\\\n 0.37... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.014 & 0.129 \\\\\n 0.458 & 0.087 \\\\\n 0.54 & 0.608 \\\\\n 0.579 & 0.689 \\\\\n 0.60... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.025 & 0.496 \\\\\n 0.342 & 0. \\\\\n 0.666 & 0.06 \\\\\n 0.682 & 0.388... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.537 & 0.049 \\\\\n 0.538 & 0.59 \\\\\n 0.902 & 0.419 \\\\\n 0.931 & 0.635 \\\\\n 0.97... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.298 & 0.866 \\\\\n 0.445 & 0.985 \\\\\n 0.507 & 0.407 \\\\\n 0.649 & 0.999 \\\\\n 0.6... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.359 & 0.994 \\\\\n 0.373 & 0.534 \\\\\n 0.399 & 0.56 \\\\\n 0.55 & 0.364 \\\\\n\\end{... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.016 & 0.765 \\\\\n 0.663 & 0.339 \\\\\n 0.718 & 0.192 \\\\\n 0.739 & 0.859 \\\\\n 0.8... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.141 & 0.81 \\\\\n 0.394 & 0.298 \\\\\n 0.661 & 0.278 \\\\\n 0.711 & 0.65 \\\\\n\\end{... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.345 & 0.763 \\\\\n -0.333 & 0.001 \\\\\n 0. & 0. \\\\\n 0.152 & 0.95 \\\\\n 0.211 & ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.16 & 0.239 \\\\\n 0.398 & 0.667 \\\\\n 0.611 & 0.998 \\\\\n\\end{array}\n\\right)$. E... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.466 & 0.406 \\\\\n -0.433 & 0.295 \\\\\n -0.352 & 0.212 \\\\\n -0.141 & 0.454 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.031 & 0.901 \\\\\n 0.217 & 0.059 \\\\\n 0.374 & 0.767 \\\\\n 0.43 & 0.828 \\\\\n 0.64... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.296 & 0.519 \\\\\n -0.248 & 0.429 \\\\\n -0.219 & 0.944 \\\\\n 0. & 0. \\\\\n 0.112 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.491 & 0.756 \\\\\n 0.648 & 0.541 \\\\\n 0.862 & 0.655 \\\\\n 0.945 & 0.815 \\\\\n\\en... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.543 & 0.395 \\\\\n -0.373 & 0.144 \\\\\n 0. & 0. \\\\\n 0.066 & 0.182 \\\\\n 0.124 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.769 & 0.485 \\\\\n -0.754 & 0.68 \\\\\n -0.523 & 0.11 \\\\\n -0.519 & 0.804 \\\\\n -... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.047 & 0.144 \\\\\n 0.127 & 0.879 \\\\\n 0.344 & 0.465 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.642 & 0.571 \\\\\n -0.441 & 0.202 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.162 & 0.132 \\\\\n 0.246 & 0.197 \\\\\n 0.327 & 0.524 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.006 & 0.201 \\\\\n 0.118 & 0.943 \\\\\n 0.737 & 0.224 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.049 & 0.573 \\\\\n 0.287 & 0.144 \\\\\n 0.501 & 0.227 \\\\\n 0.668 & 0.374 \\\\\n 0.6... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.03 & 0.162 \\\\\n 0.05 & 0.978 \\\\\n 0.191 & 0.781 \\\\\n 0.456 & 0.868 \\\\\n 0.576... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.366 & 0.132 \\\\\n 0.459 & 0.104 \\\\\n 0.475 & 0.821 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.28 & 0.777 \\\\\n -0.267 & 0.503 \\\\\n -0.069 & 0.014 \\\\\n -0.028 & 0.869 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.497 & 0.962 \\\\\n 0.719 & 0.739 \\\\\n 0.743 & 0.278 \\\\\n 0.793 & 0.28 \\\\\n 0.81... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.769 & 0.682 \\\\\n -0.761 & 0.595 \\\\\n -0.643 & 0.088 \\\\\n 0. & 0. \\\\\n\\end{a... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.252 & 0.271 \\\\\n 0.322 & 0.21 \\\\\n 0.664 & 0.343 \\\\\n 0.82 & 0.832 \\\\\n\\end{... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.825 & 0.391 \\\\\n -0.452 & 0.107 \\\\\n -0.349 & 0.081 \\\\\n 0. & 0. \\\\\n 0.064 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.417 & 0.646 \\\\\n 0.465 & 0.369 \\\\\n 0.928 & 0.649 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.258 & 0.134 \\\\\n -0.254 & 0.247 \\\\\n -0.23 & 0.522 \\\\\n -0.029 & 0.728 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.008 & 0.993 \\\\\n 0.345 & 0.7 \\\\\n 0.401 & 0.569 \\\\\n 0.533 & 0.305 \\\\\n 0.615... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.553 & 0.317 \\\\\n -0.545 & 0.568 \\\\\n -0.53 & 0.209 \\\\\n -0.454 & 0.828 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.086 & 0.821 \\\\\n 0.42 & 0.815 \\\\\n 0.47 & 0.605 \\\\\n 0.533 & 0.434 \\\\\n 0.577... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.009 & 0.281 \\\\\n 0. & 0. \\\\\n 0.085 & 0.389 \\\\\n 0.17 & 0.062 \\\\\n 0.561 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.081 & 0.326 \\\\\n 0.174 & 0.424 \\\\\n 0.328 & 0.557 \\\\\n 0.373 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.051 & 0.803 \\\\\n 0.066 & 0.474 \\\\\n 0.166 & 0.339 \\\\\n 0.362 & 0.864 \\\\\n 0.4... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.074 & 0.899 \\\\\n 0.139 & 0.263 \\\\\n 0.14 & 0.004 \\\\\n 0.254 & 0.649 \\\\\n 0.33... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.136 & 0.121 \\\\\n 0.406 & 0.242 \\\\\n 0.439 & 0.123 \\\\\n 0.596 & 0.066 \\\\\n 0.6... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.071 & 0.1 \\\\\n 0.146 & 0.493 \\\\\n 0.314 & 0.154 \\\\\n 0.461 & 0.962 \\\\\n 0.641... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.078 & 0.495 \\\\\n 0.098 & 0.331 \\\\\n 0.152 & 0.536 \\\\\n 0.213 & 0.973 \\\\\n 0.4... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.176 & 0.449 \\\\\n -0.152 & 0.688 \\\\\n -0.147 & 0.319 \\\\\n -0.044 & 0.875 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.087 & 0.223 \\\\\n -0.063 & 0.071 \\\\\n 0. & 0. \\\\\n 0.274 & 0.918 \\\\\n 0.41 & ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.144 & 0.571 \\\\\n 0.32 & 0.007 \\\\\n 0.502 & 0.35 \\\\\n 0.905 & 0.511 \\\\\n\\end{... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.72 & 0.665 \\\\\n -0.707 & 0.268 \\\\\n -0.612 & 0.071 \\\\\n -0.505 & 0.819 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.256 & 0.925 \\\\\n 0.384 & 0.6 \\\\\n 0.629 & 0.339 \\\\\n\\end{array}\n\\right)$. Es... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.019 & 0.918 \\\\\n 0. & 0. \\\\\n 0.076 & 0.88 \\\\\n 0.279 & 0.766 \\\\\n 0.348 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.037 & 0.131 \\\\\n 0.346 & 0.426 \\\\\n 0.373 & 0.239 \\\\\n 0.491 & 0.552 \\\\\n 0.5... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.443 & 0.965 \\\\\n -0.35 & 0.192 \\\\\n -0.335 & 0.933 \\\\\n -0.132 & 0.007 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.066 & 0.828 \\\\\n 0.117 & 0.98 \\\\\n 0.235 & 0.192 \\\\\n 0.261 & 0.108 \\\\\n 0.38... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.263 & 0.781 \\\\\n -0.239 & 0.342 \\\\\n -0.189 & 0.268 \\\\\n 0. & 0. \\\\\n 0.038 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.438 & 0.144 \\\\\n 0. & 0. \\\\\n 0.052 & 0.007 \\\\\n\\end{array}\n\\right)$. Estim... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.433 & 0.729 \\\\\n -0.35 & 0.352 \\\\\n -0.286 & 0.17 \\\\\n 0. & 0. \\\\\n 0.29 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.203 & 0.33 \\\\\n 0.342 & 0.864 \\\\\n 0.444 & 0.978 \\\\\n 0.513 & 0.171 \\\\\n 0.67... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.549 & 0.031 \\\\\n -0.458 & 0.159 \\\\\n -0.37 & 0.254 \\\\\n -0.042 & 0.329 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.03 & 0.52 \\\\\n 0.208 & 0.295 \\\\\n 0.358 & 0.276 \\\\\n 0.49 & 0.397 \\\\\n 0.503 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.129 & 0.732 \\\\\n 0.442 & 0.317 \\\\\n 0.905 & 0.705 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.048 & 0.772 \\\\\n 0.569 & 0.568 \\\\\n 0.653 & 0.1 \\\\\n 0.971 & 0.127 \\\\\n\\end{... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.21 & 0.955 \\\\\n 0.396 & 0.025 \\\\\n 0.663 & 0.56 \\\\\n\\end{array}\n\\right)$. Es... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.084 & 0.964 \\\\\n 0.273 & 0.208 \\\\\n 0.274 & 0.129 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.136 & 0.124 \\\\\n -0.063 & 0.423 \\\\\n 0. & 0. \\\\\n 0.122 & 0.872 \\\\\n 0.276 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.079 & 0.698 \\\\\n 0.351 & 0.173 \\\\\n 0.351 & 0.128 \\\\\n 0.397 & 0.33 \\\\\n 0.50... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.104 & 0.233 \\\\\n 0.413 & 0.079 \\\\\n 0.828 & 0.191 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.244 & 0.063 \\\\\n -0.209 & 0.405 \\\\\n -0.074 & 0.799 \\\\\n 0. & 0. \\\\\n 0.219 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.542 & 0.361 \\\\\n 0.898 & 0.556 \\\\\n\\end{array}\n\\right)$. Estima... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.527 & 0.269 \\\\\n -0.499 & 0.385 \\\\\n -0.401 & 0.383 \\\\\n -0.179 & 0.065 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.578 & 0.553 \\\\\n 0.826 & 0.787 \\\\\n 0.993 & 0.113 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.663 & 0.603 \\\\\n -0.588 & 0.652 \\\\\n -0.455 & 0.392 \\\\\n -0.208 & 0.783 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.233 & 0.828 \\\\\n 0.362 & 0.339 \\\\\n 0.429 & 0.603 \\\\\n 0.476 & 0.814 \\\\\n 0.6... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.432 & 0.445 \\\\\n 0.648 & 0.854 \\\\\n 0.733 & 0.537 \\\\\n 0.791 & 0.179 \\\\\n 0.9... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.316 & 0.157 \\\\\n 0.399 & 0.498 \\\\\n 0.512 & 0.793 \\\\\n 0.682 & 0.494 \\\\\n 0.7... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.27 & 0.799 \\\\\n 0.464 & 0.791 \\\\\n 0.527 & 0.178 \\\\\n 0.589 & 0.651 \\\\\n 0.60... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.415 & 0.082 \\\\\n 0.641 & 0.811 \\\\\n 0.956 & 0.768 \\\\\n 0.992 & 0.691 \\\\\n\\en... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.648 & 0.588 \\\\\n -0.351 & 0.165 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.076 & 0.097 \\\\\n -0.016 & 0.263 \\\\\n 0. & 0. \\\\\n 0.197 & 0.625 \\\\\n 0.444 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.275 & 0.888 \\\\\n 0.435 & 0.338 \\\\\n 0.544 & 0.187 \\\\\n 0.564 & 0.46 \\\\\n 0.87... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.094 & 0.543 \\\\\n 0.104 & 0.76 \\\\\n 0.203 & 0.911 \\\\\n 0.331 & 0.364 \\\\\n 0.44... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.426 & 0.77 \\\\\n 0.702 & 0.608 \\\\\n 0.81 & 0.166 \\\\\n\\end{array}... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.231 & 0.001 \\\\\n 0.355 & 0.774 \\\\\n 0.401 & 0.163 \\\\\n\\end{arra... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.137 & 0.617 \\\\\n 0.163 & 0.915 \\\\\n 0.328 & 0.993 \\\\\n 0.334 & 0.006 \\\\\n 0.4... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.074 & 0.849 \\\\\n 0.392 & 0.885 \\\\\n 0.521 & 0.983 \\\\\n 0.638 & 0.62 \\\\\n 0.73... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.827 & 0.748 \\\\\n -0.28 & 0.378 \\\\\n -0.19 & 0.269 \\\\\n 0. & 0. \\\\\n\\end{arr... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.162 & 0.8 \\\\\n 0.237 & 0.26 \\\\\n 0.253 & 0.199 \\\\\n 0.295 & 0.682 \\\\\n 0.395 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.078 & 0.623 \\\\\n 0.46 & 0.408 \\\\\n 0.501 & 0.055 \\\\\n 0.528 & 0.748 \\\\\n 0.85... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.018 & 0.434 \\\\\n 0.143 & 0.482 \\\\\n 0.236 & 0.476 \\\\\n 0.393 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.015 & 0.299 \\\\\n 0.092 & 0.305 \\\\\n 0.1 & 0.16 \\\\\n 0.405 & 0.429 \\\\\n 0.697 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.229 & 0.209 \\\\\n 0. & 0. \\\\\n 0.372 & 0.156 \\\\\n 0.585 & 0.126 \\\\\n\\end{arr... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.23 & 0.468 \\\\\n -0.207 & 0.511 \\\\\n -0.043 & 0.446 \\\\\n 0. & 0. \\\\\n\\end{ar... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.003 & 0.725 \\\\\n 0.134 & 0.033 \\\\\n 0.147 & 0.436 \\\\\n 0.232 & 0.132 \\\\\n 0.5... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.17 & 0.114 \\\\\n -0.155 & 0.788 \\\\\n -0.118 & 0.803 \\\\\n 0. & 0. \\\\\n 0.116 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.312 & 0.392 \\\\\n 0.382 & 0.128 \\\\\n 0.435 & 0.309 \\\\\n 0.444 & 0.187 \\\\\n 0.5... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.008 & 0.706 \\\\\n 0.047 & 0.014 \\\\\n 0.107 & 0.331 \\\\\n 0.248 & 0.692 \\\\\n 0.2... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.325 & 0.561 \\\\\n 0.531 & 0.153 \\\\\n 0.737 & 0.305 \\\\\n\\end{arra... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.481 & 0.208 \\\\\n -0.024 & 0.661 \\\\\n 0. & 0. \\\\\n 0.161 & 0.038 \\\\\n\\end{ar... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.043 & 0.178 \\\\\n 0.319 & 0.474 \\\\\n 0.365 & 0.265 \\\\\n 0.378 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.326 & 0.332 \\\\\n -0.295 & 0.031 \\\\\n -0.11 & 0.775 \\\\\n -0.003 & 0.882 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.524 & 0.758 \\\\\n 0.622 & 0.255 \\\\\n 0.906 & 0.267 \\\\\n 0.908 & 0.839 \\\\\n\\en... | geometry | polygons |
End of preview. Expand in Data Studio
Khan Math – Geometry
Geometry problems from Khan Academy in ChatML format. Covers triangles, circles, coordinate geometry, and more.
Quick Start
from datasets import load_dataset
dataset = load_dataset("NecroMOnk/khan-math-geometry")
print(dataset["train"][0])
Example record:
{
"messages": [
{"role": "system", "content": "You are a mathematics tutor. Answer the following math problem."},
{"role": "user", "content": "Find the arclength of the function $f(x) = \\log(2x)$ on the interval $x=4$ to $x=5$"},
{"role": "assistant", "content": "$-\\sqrt{17}+\\sqrt{26}+\\tanh^{-1}\\left(\\sqrt{17}\\right)-\\tanh^{-1}\\left(\\sqrt{26}\\right)$"}
],
"topic": "calculus",
"subtopic": "arclength"
}
Dataset Stats
- 300K problems
- ChatML format
- Source: Khan Academy geometry materials
- Language: English
- Math notation: LaTeX
Fields
| Field | Type | Description |
|---|---|---|
messages |
list | ChatML turns: system, user, assistant |
topic |
string | Top-level math topic (e.g. calculus) |
subtopic |
string | Specific subtopic (e.g. arclength) |
Source
Problems sourced from Khan Academy via the AMPS dataset. Problems and answers are in LaTeX format.
Versions
- v1 – raw extraction, minor artifacts possible (e.g. degenerate intervals,
+-notation) - v2 – cleaned formulas, extraction artifacts removed (coming soon)
- Downloads last month
- 7