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Jan
29
awarded  Nice Answer
Dec
29
comment Past open problems with sudden and easy-to-understand solutions
Fisk's proof is based on the fact that a simple plane polygon can be triangulated using diagonals between existing vertices. The fact that this is possible to not that hard (though there were incorrect proofs in the past) but an "easier" proof using the notion of an ear of a polygon was developed by Gary Meisters, who died about a month ago. Meisters' showed that polygons with 4 or more vertices have at least two ears made it possible to use induction to prove that simple polygons can be triangulated: legacy.com/obituaries/coloradoan/…
Dec
29
comment Past open problems with sudden and easy-to-understand solutions
The original question was asked by Sylvester and years later Erdos asked the question in the dual form - the problem can be thought of as being in the projective plane. Tibor Gallai provided an answer and later Kelly a very elegant metrical proof. However, there was an even simpler proof buried in Deutsche Mathematik, published by the Nazis. This proof by Eberhard Melchior was a combinatorial proof more in keeping with Sylvester's original setting. More details are here: en.wikipedia.org/wiki/Sylvester%E2%80%93Gallai_theorem
Dec
24
answered Past open problems with sudden and easy-to-understand solutions
Aug
20
awarded  Yearling
Jul
11
answered Extension of Descartes' “Kissing Circles” Theorem
Sep
27
comment Good Reference for Justifying (less well-known fields of) Math?
This is a wonderfully rich book which looks at mathematics from many perspectives and, thus, gives a picture of the subject that while having a certain "random" quality is also very nuanced. As one reads more of the specialized essays one comes to see the way different aspects of the subject, from its theory to its applications, to the extraordinary people from many countries and cultures who contributed to it, make mathematics an exciting and wonderfully rich subject.
Sep
24
awarded  Autobiographer
Sep
12
comment Periodicity with irrational numbers
You might look here: en.wikipedia.org/wiki/Beatty_sequence
Sep
5
awarded  Nice Answer
Aug
26
answered Knots and graphs
Aug
20
awarded  Yearling
Jul
24
answered Mathematical conjectures believed to be false
Jul
19
comment Space-filling polyhedra (or honeycomb) survey?
For tetrahedra, have you seen: Senechal, Marjorie. "Which tetrahedra fill space?." Mathematics Magazine (1981): 227-243.
Jul
10
answered Why do people lose in chess?
Jun
24
answered What is the realization of a graph in $\mathbb{R}^d$?
Jun
23
answered Why is the 24-cell (also called Icositetrachoron or Hyperdiamond) the unique regular convex polychoron which has no direct three-dimensional analog?
Jun
21
answered Order Types, Point-line duality
Jun
7
answered Applications of Finite Projective Planes
May
12
answered Surface Geometry