# Hexagrammum Mysticum

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Consider six points on a conic section (circle, ellipse, parabola or hyperbola). Label them B L A I S E and connect them to form a hexagon. There are 15 ways to choose two points, leading to 15 lines that intersect at 45 points.

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Contributed by: Ed Pegg Jr (August 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Points are sometimes called nodes, giving the N part of N(BLAISE), N(BAS.LIE) and N(BL.AI.SE) in the Kirkman, Steiner and Salmon points.

References

[1] Wikipedia. "Pascal's Theorem." (Aug 21, 2017) en.wikipedia.org/wiki/Pascal%27 s_theorem.

[2] Wikipedia. "Blaise Pascal." (Aug 21, 2017) en.wikipedia.org/wiki/Blaise_Pascal.

[3] Wikipedia. "Thomas Kirkman." (Aug 21, 2017) en.wikipedia.org/wiki/Thomas_Kirkman.

[4] Wikipedia. "Arthur Cayley." (Aug 21, 2017) en.wikipedia.org/wiki/Arthur_Cayley.

[5] Wikipedia. "Jakob Steiner." (Aug 21, 2017) en.wikipedia.org/wiki/Jakob_Steiner.

[6] Wikipedia. "Julius Plücker." (Aug 21, 2017) en.wikipedia.org/wiki/Julius_Pl%C3%BCcker.

[7] Wikipedia. "George Salmon." (Aug 21, 2017) en.wikipedia.org/wiki/George_Salmon.

[8] J. Conway and A. Ryba, "The Pascal Mysticum Demystified," *The Mathematical Intelligencer*, 34(3), 2012 pp. 4–8. doi:10.1007/s00283-012-9301-4.

## Permanent Citation

"Hexagrammum Mysticum"

http://demonstrations.wolfram.com/HexagrammumMysticum/

Wolfram Demonstrations Project

Published: August 24 2017