Datasets:
ai-metrology-lab
/
MathBode-SimilarTriangles

Dataset card Data Studio Files
xet
 Community
family
stringclasses
1 value
question_id
int64
0
2
signal_type
stringclasses
2 values
amplitude_scale
float64
0.5
2.5
frequency_cycles
float64
1
16
phase_deg
float64
0
240
⌀
time_step
int64
0
255
p_value
float64
2.25
2.75
prompt
stringlengths
157
173
ground_truth
float64
18
41.3
symbolic_baseline_answer
float64
18
41.3
similar_triangles
1
sinusoid
0.5
8
0
48
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
8
0
49
2.535355
Two triangles are similar with ratio 2.5353553390593273:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.282843
20.282843
similar_triangles
1
sinusoid
0.5
8
0
50
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
8
0
51
2.535355
Two triangles are similar with ratio 2.5353553390593273:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.282843
20.282843
similar_triangles
1
sinusoid
0.5
8
0
52
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
8
0
53
2.464645
Two triangles are similar with ratio 2.4646446609406727:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.717157
19.717157
similar_triangles
1
sinusoid
0.5
8
0
54
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
8
0
55
2.464645
Two triangles are similar with ratio 2.4646446609406727:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.717157
19.717157
similar_triangles
1
sinusoid
0.5
8
0
56
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
8
0
57
2.535355
Two triangles are similar with ratio 2.5353553390593273:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.282843
20.282843
similar_triangles
1
sinusoid
0.5
8
0
58
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
8
0
59
2.535355
Two triangles are similar with ratio 2.5353553390593273:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.282843
20.282843
similar_triangles
1
sinusoid
0.5
8
0
60
2.5
Two triangles are similar with ratio 2.5000000000000004:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
8
0
61
2.464645
Two triangles are similar with ratio 2.4646446609406727:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.717157
19.717157
similar_triangles
1
sinusoid
0.5
8
0
62
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
8
0
63
2.464645
Two triangles are similar with ratio 2.4646446609406727:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.717157
19.717157
similar_triangles
1
sinusoid
0.5
16
0
0
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
1
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
2
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
3
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
4
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
5
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
6
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
7
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
8
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
9
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
10
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
11
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
12
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
13
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
14
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
15
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
16
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
17
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
18
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
19
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
20
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
21
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
22
2.5
Two triangles are similar with ratio 2.5000000000000004:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
23
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
24
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
25
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
26
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
27
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
28
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
29
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
30
2.5
Two triangles are similar with ratio 2.5000000000000004:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
31
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
32
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
33
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
34
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
35
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
36
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
37
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
38
2.5
Two triangles are similar with ratio 2.5000000000000004:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
39
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
40
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
41
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
42
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
43
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
44
2.5
Two triangles are similar with ratio 2.4999999999999996:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
45
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
46
2.5
Two triangles are similar with ratio 2.5000000000000004:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
47
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
48
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
49
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
50
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
51
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
52
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
53
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
54
2.5
Two triangles are similar with ratio 2.5000000000000004:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
55
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
56
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
57
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
58
2.5
Two triangles are similar with ratio 2.5:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
59
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
16
0
60
2.5
Two triangles are similar with ratio 2.4999999999999996:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
61
2.55
Two triangles are similar with ratio 2.55:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.4
20.4
similar_triangles
1
sinusoid
0.5
16
0
62
2.5
Two triangles are similar with ratio 2.5000000000000004:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20
20
similar_triangles
1
sinusoid
0.5
16
0
63
2.45
Two triangles are similar with ratio 2.45:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.6
19.6
similar_triangles
1
sinusoid
0.5
1
120
0
2.543301
Two triangles are similar with ratio 2.543301270189222:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.34641
20.34641
similar_triangles
1
sinusoid
0.5
1
120
1
2.540642
Two triangles are similar with ratio 2.540642334229581:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.325139
20.325139
similar_triangles
1
sinusoid
0.5
1
120
2
2.537592
Two triangles are similar with ratio 2.537591990373949:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.300736
20.300736
similar_triangles
1
sinusoid
0.5
1
120
3
2.53418
Two triangles are similar with ratio 2.5341796151011438:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.273437
20.273437
similar_triangles
1
sinusoid
0.5
1
120
4
2.530438
Two triangles are similar with ratio 2.530438071450436:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.243505
20.243505
similar_triangles
1
sinusoid
0.5
1
120
5
2.526403
Two triangles are similar with ratio 2.526403392532518:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.211227
20.211227
similar_triangles
1
sinusoid
0.5
1
120
6
2.522114
Two triangles are similar with ratio 2.52211443451095:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.176915
20.176915
similar_triangles
1
sinusoid
0.5
1
120
7
2.517613
Two triangles are similar with ratio 2.517612502396062:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.1409
20.1409
similar_triangles
1
sinusoid
0.5
1
120
8
2.512941
Two triangles are similar with ratio 2.5129409522551263:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.103528
20.103528
similar_triangles
1
sinusoid
0.5
1
120
9
2.508145
Two triangles are similar with ratio 2.5081447736697293:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.065158
20.065158
similar_triangles
1
sinusoid
0.5
1
120
10
2.50327
Two triangles are similar with ratio 2.503270156461507:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
20.026161
20.026161
similar_triangles
1
sinusoid
0.5
1
120
11
2.498364
Two triangles are similar with ratio 2.4983640458589114:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.986912
19.986912
similar_triangles
1
sinusoid
0.5
1
120
12
2.493474
Two triangles are similar with ratio 2.4934736903889974:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.94779
19.94779
similar_triangles
1
sinusoid
0.5
1
120
13
2.488646
Two triangles are similar with ratio 2.4886461868482814:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.909169
19.909169
similar_triangles
1
sinusoid
0.5
1
120
14
2.483928
Two triangles are similar with ratio 2.483928026734842:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.871424
19.871424
similar_triangles
1
sinusoid
0.5
1
120
15
2.479365
Two triangles are similar with ratio 2.4793646485097804:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.834917
19.834917
similar_triangles
1
sinusoid
0.5
1
120
16
2.475
Two triangles are similar with ratio 2.475:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.8
19.8
similar_triangles
1
sinusoid
0.5
1
120
17
2.470876
Two triangles are similar with ratio 2.47087611515661:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.767009
19.767009
similar_triangles
1
sinusoid
0.5
1
120
18
2.467033
Two triangles are similar with ratio 2.4670327092449966:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.736262
19.736262
similar_triangles
1
sinusoid
0.5
1
120
19
2.463507
Two triangles are similar with ratio 2.4635067963651083:1. If the smaller triangle has side length 8, what is the corresponding side length of the larger triangle? FINAL:
19.708054
19.708054