Mathologer: Times Tables, Mandelbrot, and the Heart of Mathematics
Expression 6: "C" Subscript, "A" , Baseline equals cosine left parenthesis, StartFraction, 2 pi "A" Over "n" , EndFraction , right parenthesisCA=cos2πAn
equals=
11
0.9 1 3 5 4 5 4 5 7 6 4 30.913545457643
0.6 6 9 1 3 0 6 0 6 3 5 90.669130606359
0.3 0 9 0 1 6 9 9 4 3 7 50.309016994375
negative 0.1 0 4 5 2 8 4 6 3 2 6 8−0.104528463268
negative 0.5−0.5
negative 0.8 0 9 0 1 6 9 9 4 3 7 5−0.809016994375
negative 0.9 7 8 1 4 7 6 0 0 7 3 4−0.978147600734
negative 0.9 7 8 1 4 7 6 0 0 7 3 4−0.978147600734
negative 0.8 0 9 0 1 6 9 9 4 3 7 5−0.809016994375
negative 0.5−0.5
negative 0.1 0 4 5 2 8 4 6 3 2 6 8−0.104528463268
0.3 0 9 0 1 6 9 9 4 3 7 50.309016994375
0.6 6 9 1 3 0 6 0 6 3 5 90.669130606359
0.9 1 3 5 4 5 4 5 7 6 4 30.913545457643
6
Expression 7: "S" Subscript, "A" , Baseline equals sine left parenthesis, StartFraction, 2 pi "A" Over "n" , EndFraction , right parenthesisSA=sin2πAn
equals=
00
0.4 0 6 7 3 6 6 4 3 0 7 60.406736643076
0.7 4 3 1 4 4 8 2 5 4 7 70.743144825477
0.9 5 1 0 5 6 5 1 6 2 9 50.951056516295
0.9 9 4 5 2 1 8 9 5 3 6 80.994521895368
0.8 6 6 0 2 5 4 0 3 7 8 40.866025403784
0.5 8 7 7 8 5 2 5 2 2 9 20.587785252292
0.2 0 7 9 1 1 6 9 0 8 1 80.207911690818
negative 0.2 0 7 9 1 1 6 9 0 8 1 8−0.207911690818
negative 0.5 8 7 7 8 5 2 5 2 2 9 2−0.587785252292
negative 0.8 6 6 0 2 5 4 0 3 7 8 4−0.866025403784
negative 0.9 9 4 5 2 1 8 9 5 3 6 8−0.994521895368
negative 0.9 5 1 0 5 6 5 1 6 2 9 5−0.951056516295
negative 0.7 4 3 1 4 4 8 2 5 4 7 7−0.743144825477
negative 0.4 0 6 7 3 6 6 4 3 0 7 6−0.406736643076
7
Hidden Label: left parenthesis, "C" Subscript, "A" , Baseline , "S" Subscript, "A" , Baseline , right parenthesisCA,SA
Label
equals=
left parenthesis, 1 , 0 , right parenthesis1,0
left parenthesis, 0.9 1 3 5 , 0.4 0 6 7 , right parenthesis0.9135,0.4067
left parenthesis, 0.6 6 9 1 , 0.7 4 3 1 , right parenthesis0.6691,0.7431
left parenthesis, 0.3 0 9 , 0.9 5 1 1 , right parenthesis0.309,0.9511
left parenthesis, negative 0.1 0 4 5 , 0.9 9 4 5 , right parenthesis−0.1045,0.9945
left parenthesis, negative 0.5 , 0.8 6 6 , right parenthesis−0.5,0.866
left parenthesis, negative 0.8 0 9 , 0.5 8 7 8 , right parenthesis−0.809,0.5878
left parenthesis, negative 0.9 7 8 1 , 0.2 0 7 9 , right parenthesis−0.9781,0.2079
left parenthesis, negative 0.9 7 8 1 , negative 0.2 0 7 9 , right parenthesis−0.9781,−0.2079
left parenthesis, negative 0.8 0 9 , negative 0.5 8 7 8 , right parenthesis−0.809,−0.5878
left parenthesis, negative 0.5 , negative 0.8 6 6 , right parenthesis−0.5,−0.866
left parenthesis, negative 0.1 0 4 5 , negative 0.9 9 4 5 , right parenthesis−0.1045,−0.9945
left parenthesis, 0.3 0 9 , negative 0.9 5 1 1 , right parenthesis0.309,−0.9511
left parenthesis, 0.6 6 9 1 , negative 0.7 4 3 1 , right parenthesis0.6691,−0.7431
left parenthesis, 0.9 1 3 5 , negative 0.4 0 6 7 , right parenthesis0.9135,−0.4067
8
Expression 9: "C" Subscript, "B" , Baseline equals cosine left parenthesis, StartFraction, 2 pi "B" Over "n" , EndFraction , right parenthesisCB=cos2πBn
equals=
11
0.6 6 9 1 3 0 6 0 6 3 5 90.669130606359
negative 0.1 0 4 5 2 8 4 6 3 2 6 8−0.104528463268
negative 0.8 0 9 0 1 6 9 9 4 3 7 5−0.809016994375
negative 0.9 7 8 1 4 7 6 0 0 7 3 4−0.978147600734
negative 0.5−0.5
0.3 0 9 0 1 6 9 9 4 3 7 50.309016994375
0.9 1 3 5 4 5 4 5 7 6 4 30.913545457643
0.9 1 3 5 4 5 4 5 7 6 4 30.913545457643
0.3 0 9 0 1 6 9 9 4 3 7 50.309016994375
negative 0.5−0.5
negative 0.9 7 8 1 4 7 6 0 0 7 3 4−0.978147600734
negative 0.8 0 9 0 1 6 9 9 4 3 7 5−0.809016994375
negative 0.1 0 4 5 2 8 4 6 3 2 6 8−0.104528463268
0.6 6 9 1 3 0 6 0 6 3 5 90.669130606359
9
Expression 10: "S" Subscript, "B" , Baseline equals sine left parenthesis, StartFraction, 2 pi "B" Over "n" , EndFraction , right parenthesisSB=sin2πBn
equals=
00
0.7 4 3 1 4 4 8 2 5 4 7 70.743144825477
0.9 9 4 5 2 1 8 9 5 3 6 80.994521895368
0.5 8 7 7 8 5 2 5 2 2 9 20.587785252292
negative 0.2 0 7 9 1 1 6 9 0 8 1 8−0.207911690818
negative 0.8 6 6 0 2 5 4 0 3 7 8 4−0.866025403784
negative 0.9 5 1 0 5 6 5 1 6 2 9 5−0.951056516295
negative 0.4 0 6 7 3 6 6 4 3 0 7 6−0.406736643076
0.4 0 6 7 3 6 6 4 3 0 7 60.406736643076
0.9 5 1 0 5 6 5 1 6 2 9 50.951056516295
0.8 6 6 0 2 5 4 0 3 7 8 40.866025403784
0.2 0 7 9 1 1 6 9 0 8 1 80.207911690818
negative 0.5 8 7 7 8 5 2 5 2 2 9 2−0.587785252292
negative 0.9 9 4 5 2 1 8 9 5 3 6 8−0.994521895368
negative 0.7 4 3 1 4 4 8 2 5 4 7 7−0.743144825477
10
Expression 11: left parenthesis, "C" Subscript, "A" , Baseline "t" plus left parenthesis, 1 minus "t" , right parenthesis "C" Subscript, "B" , Baseline , "S" Subscript, "A" , Baseline "t" plus left parenthesis, 1 minus "t" , right parenthesis "S" Subscript, "B" , Baseline , right parenthesisCAt+1−tCB,SAt+1−tSB
domain t Minimum: 00
less than or equal to "t" less than or equal to≤t≤
