Math General Knowledge #2

A polychoron is a 4-dimensional polyhedron. Alternate names for those are accepted.

See also: Math General Knowledge, by Aquarius17

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Last updated: April 14, 2017

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First submitted	August 7, 2015
Times taken	82
Average score	17.1%
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Hint	Answer
Number of regular plane tesselations	3
Number of semi-regular plane tesselations	8
Number of Archimedean solids	13
Regular polychora	Pentachoron
	Octachoron
	Hexadecachoron
	Icositetrachoron
	Hecatonicosachoron
	Hexacosichoron
Reflection of the median across the angle bisector	Symmedian
Isogonal conjugate of the circumcentre	Orthocentre
Circumcircle of the midpoints of the sides of a triangle	Nine point circle
Result of colouring Pascal's triangle by parity	Sierpinski's triangle
Pascal's first name	Blaise
States that Pythagorean triples with higher exponents do not exist	Fermat's Last Theorem
States that a^b - c^d = 1 has only 1 integer solution when all 4 variables are greater than 1	Catalan's Conjecture
	Mihăilescu's Theorem
A prime p, where 2p+1 is prime	Sophie Germain prime
States that there exist arbitrarily long arithmetic progressions of prime numbers	Green-Tao Theorem
What the "fi" in Fibonacci stands for	filius
Fibonacci sequence, but starting with 2, 1, ...	Lucas numbers
States that a spherical triangle on a unit sphere has area equal to the sum of its angles, minus pi	Girard's Theorem
States that two triangles are in perspective axially if and only if they are in perspective centrally	Desargues' Theorem
Namesake of the Cartesian plane (first name required)	René Descartes
Reflection of a complex number across the real axis	conjugate
States that any continuous function mapping a compact convex non-empty set into itself maps a point to itself	Brouwer's fixed point theorem
4-dimensional extension of complex numbers	Quaternions
Euler Characteristic of a torus	0
Loop that, when chopped in half, remains a loop	Möbius strip
Object that, when chopped in half, gives the previous answer	Klein bottle
The product of a gross, a dozen, and a score	34560
A non-disjoint graph whose vertices all have even degree contains an...	Eulerian circuit
French Mathematician; died aged 20 from a duel	Évariste Galois
Alice in Wonderland author (pen and real names)	Lewis Carroll
Alice in Wonderland author (pen and real names)	Charles Lutwidge Dodgson

Level 85

Aug 7, 2015

The empty set is both convex and compact, but no continuous function maps a point of it to itself.

Level 60

Aug 7, 2015

The empty set is an interesting edge case...I'll modify the description

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