A374971 -id:A374971 - cp's OEIS frontend

A374972 Decimal expansion of the sagitta of a regular heptagon with unit side length.

1, 1, 4, 1, 2, 1, 7, 3, 7, 1, 9, 5, 0, 7, 4, 9, 6, 9, 0, 3, 8, 8, 0, 5, 6, 8, 1, 0, 3, 0, 5, 0, 7, 3, 9, 1, 3, 6, 9, 3, 9, 0, 8, 4, 0, 4, 9, 0, 1, 7, 6, 3, 1, 8, 9, 8, 9, 8, 4, 4, 4, 5, 9, 8, 0, 1, 9, 1, 2, 4, 2, 7, 8, 5, 6, 9, 4, 0, 9, 3, 9, 4, 5, 7, 3, 4, 6, 9, 3, 5

Offset: 0

Paolo Xausa, Jul 26 2024

			0.114121737195074969038805681030507391369390840490...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Eric Weisstein's World of Mathematics, Sagitta.
Index entries for algebraic numbers, degree 6.

Cf. A374957 (circumradius), A374971 (apothem), A178817 (area).
Cf. sagitta of other polygons with unit side length: A020769 (triangle), A174968 (square), A375068 (pentagon), A375069 (hexagon), A374972 (heptagon), A375070 (octagon), A375153 (9-gon), A375189 (10-gon), A375192 (11-gon), A375194 (12-gon).
Cf. A343059.

First[RealDigits[Tan[Pi/14]/2, 10, 100]]

tan(Pi/14)/2 \\ Charles R Greathouse IV, Feb 04 2025

polrootsreal(448*x^6-560*x^4+84*x^2-1)[4] \\ Charles R Greathouse IV, Feb 04 2025

Equals tan(Pi/14)/2 = A343059/2.

Equals A374957 - A374971.

A375067 Decimal expansion of the apothem (inradius) of a regular pentagon with unit side length.

Original entry on oeis.org

6, 8, 8, 1, 9, 0, 9, 6, 0, 2, 3, 5, 5, 8, 6, 7, 6, 9, 1, 0, 3, 6, 0, 4, 7, 9, 0, 9, 5, 5, 4, 4, 3, 8, 3, 9, 7, 6, 2, 9, 4, 9, 6, 6, 8, 0, 0, 4, 0, 7, 9, 3, 3, 1, 6, 8, 2, 8, 3, 7, 8, 8, 2, 8, 0, 9, 5, 4, 7, 5, 9, 6, 8, 8, 3, 5, 8, 6, 4, 9, 2, 5, 3, 2, 9, 7, 6, 4, 9, 6

Offset: 0

Paolo Xausa, Jul 29 2024

			0.688190960235586769103604790955443839762949668...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Wikipedia, Apothem.
Index entries for algebraic numbers, degree 4.

Cf. A300074 (circumradius), A375068 (sagitta), A102771 (area).
Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).
Cf. A019934, A019952, A019863, A131595.

Mathematica
```
First[RealDigits[Cot[Pi/5]/2, 10, 100]]
```

 5/tan(Pi/5) \\ Charles R Greathouse IV, Feb 05 2025

Equals cot(Pi/5)/2 = A019952/2.
Equals 1/(2*tan(Pi/5)) = 1/(2*A019934).
Equals sqrt(1/4 + 1/(2*sqrt(5))).
Equals (1/2)*csc(Pi/5)*cos(Pi/5) = A300074*A019863.
Equals A300074 - A375068.
Equals A131595/30. - Hugo Pfoertner, Jul 30 2024

A375152 Decimal expansion of the apothem (inradius) of a regular 9-gon with unit side length.

Original entry on oeis.org

1, 3, 7, 3, 7, 3, 8, 7, 0, 9, 7, 2, 7, 3, 1, 1, 1, 3, 9, 3, 8, 0, 8, 3, 2, 0, 1, 3, 2, 4, 8, 8, 3, 6, 3, 5, 8, 8, 7, 5, 9, 3, 6, 2, 9, 9, 5, 8, 5, 4, 1, 2, 9, 1, 0, 7, 5, 2, 6, 3, 6, 5, 0, 1, 2, 5, 9, 9, 4, 9, 1, 2, 6, 9, 4, 0, 7, 9, 6, 5, 9, 2, 1, 7, 0, 3, 0, 2, 1, 2

Offset: 1

Paolo Xausa, Aug 01 2024

			1.3737387097273111393808320132488363588759362995854...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Wikipedia, Apothem.
Index entries for algebraic numbers, degree 6.

Cf. A375151 (circumradius), A375153 (sagitta), A256853 (area).
Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).
Cf. A019879, A019918, A019968.

Mathematica
```
First[RealDigits[Cot[Pi/9]/2, 10, 100]]
```

 5/tan(Pi/9) \\ Charles R Greathouse IV, Feb 05 2025

Equals cot(Pi/9)/2 = A019968/2.
Equals 1/(2*tan(Pi/9)) = 1/(2*A019918).
Equals A375151*cos(Pi/9) = A375151*A019879.
Equals A375151 - A375153.
Largest of the 6 real-valued roots of 192*x^6 -432*x^4 +132*x^2 -1=0. - R. J. Mathar, Aug 29 2025

A375191 Decimal expansion of the apothem (inradius) of a regular 11-gon with unit side length.

Original entry on oeis.org

1, 7, 0, 2, 8, 4, 3, 6, 1, 9, 4, 4, 4, 6, 2, 5, 0, 0, 4, 5, 2, 4, 0, 6, 5, 1, 7, 3, 3, 2, 4, 4, 2, 4, 4, 1, 5, 9, 7, 8, 6, 4, 9, 9, 9, 3, 0, 6, 0, 9, 1, 4, 0, 7, 0, 4, 8, 8, 9, 6, 7, 0, 3, 0, 5, 3, 5, 9, 7, 6, 5, 3, 4, 5, 1, 3, 2, 9, 1, 0, 4, 8, 1, 1, 1, 4, 5, 7, 0, 2

Offset: 1

Paolo Xausa, Aug 04 2024

			1.702843619444625004524065173324424415978649993...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Wikipedia, Apothem.
Index entries for algebraic numbers, degree 10.

Cf. A375190 (circumradius), A375192 (sagitta), A256854 (area).

Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375193 (12-gon).

First[RealDigits[Cot[Pi/11]/2, 10, 100]]

 5/tan(Pi/11) \\ Charles R Greathouse IV, Feb 05 2025

Equals cot(Pi/11)/2.
Equals 1/(2*tan(Pi/11)).
Equals A375190*cos(Pi/11).
Equals A375190 - A375192.

A375193 Decimal expansion of the apothem (inradius) of a regular 12-gon with unit side length.

Original entry on oeis.org

1, 8, 6, 6, 0, 2, 5, 4, 0, 3, 7, 8, 4, 4, 3, 8, 6, 4, 6, 7, 6, 3, 7, 2, 3, 1, 7, 0, 7, 5, 2, 9, 3, 6, 1, 8, 3, 4, 7, 1, 4, 0, 2, 6, 2, 6, 9, 0, 5, 1, 9, 0, 3, 1, 4, 0, 2, 7, 9, 0, 3, 4, 8, 9, 7, 2, 5, 9, 6, 6, 5, 0, 8, 4, 5, 4, 4, 0, 0, 0, 1, 8, 5, 4, 0, 5, 7, 3, 0, 9

Offset: 1

Paolo Xausa, Aug 04 2024

Apart from the first digit the same as A010527.

			1.8660254037844386467637231707529361834714026269...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Wikipedia, Apothem.
Index entries for algebraic numbers, degree 2.

Cf. A188887 (circumradius), A375194 (sagitta), A178809 (area).
Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon).
Cf. A019884, A019913, A019973, A332133, A375069.

First[RealDigits[Cot[Pi/12]/2, 10, 100]]

sqrt(3)/2 + 1 \\ Charles R Greathouse IV, Feb 05 2025

Equals cot(Pi/12)/2 = (2 + sqrt(3))/2 = A019973/2.
Equals 1/(2*tan(Pi/12)) = 1/(2*A019913).
Equals A188887*cos(Pi/12) = A188887*A019884.
Equals A188887 - A375194.
Equals A332133^2 = 2 - A375069. - Hugo Pfoertner, Aug 04 2024

A374957 Decimal expansion of the circumradius of a regular heptagon with unit side length.

Original entry on oeis.org

1, 1, 5, 2, 3, 8, 2, 4, 3, 5, 4, 8, 1, 2, 4, 3, 2, 5, 2, 6, 2, 0, 5, 7, 5, 1, 1, 1, 7, 7, 3, 4, 2, 7, 5, 5, 6, 7, 2, 2, 2, 5, 0, 9, 4, 3, 8, 0, 3, 1, 6, 0, 5, 8, 1, 0, 3, 1, 5, 5, 3, 1, 4, 8, 2, 3, 3, 4, 2, 6, 6, 7, 1, 3, 8, 9, 2, 3, 9, 7, 9, 8, 1, 8, 9, 5, 5, 5, 7, 1

Offset: 1

Paolo Xausa, Jul 26 2024

			1.15238243548124325262057511177342755672225094380...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Regular Polygon.
Wikipedia, Regular polygon.
Index entries for algebraic numbers, degree 6.

Cf. A374971 (apothem), A374972 (sagitta), A178817 (area).
Cf. circumradius of other polygons with unit side length: A020760 (triangle), A010503 (square), A300074 (pentagon), A285871 (octagon), A375151 (9-gon), A001622 (10-gon), A375190 (11-gon), A188887 (12-gon).
Cf. A073052, A121598, A272487.

Mathematica
```
First[RealDigits[Csc[Pi/7]/2, 10, 100]]
```

 5/sin(Pi/7) \\ Charles R Greathouse IV, Feb 05 2025

Equals csc(Pi/7)/2 = A121598/2.
Equals 1/(2*sin(Pi/7)) = 1/A272487.
Equals A374971/cos(Pi/7) = A374971/A073052.
Largest of the 6 real-valued roots of 7*x^6-14*x^4+7*x^2-1=0. - R. J. Mathar, Aug 29 2025

cp's OEIS Frontend

A374972 Decimal expansion of the sagitta of a regular heptagon with unit side length.

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A375067 Decimal expansion of the apothem (inradius) of a regular pentagon with unit side length.

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A375152 Decimal expansion of the apothem (inradius) of a regular 9-gon with unit side length.

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A375191 Decimal expansion of the apothem (inradius) of a regular 11-gon with unit side length.

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A375193 Decimal expansion of the apothem (inradius) of a regular 12-gon with unit side length.

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A374957 Decimal expansion of the circumradius of a regular heptagon with unit side length.

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