3,959 reputation
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bio website york.cuny.edu/~malk
location New York, NY
age
visits member for 4 years, 4 months
seen Nov 15 at 17:14

I am a mathematician interested in geometry, combinatorics, mathematical modeling, and mathematics education.


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
Apr
21
comment Find the volume of triangular pyramid
If one knows the coordinates of all 4 for the vertices of the tetrahedron there is a "formula" involving determinants that allows one to find the volume of the tetrahedron.
Apr
2
answered Find a voting system - possibly Schulze Method
Mar
22
answered Maximum number of pipes used to construct the polygon
Mar
20
comment showing that all convex polehedron graphs are 3-connected
Typo in above in my statement of Steinitz's Theorem: A graph is 3-polytopal if and only it is planar and 3-connected.
Mar
20
comment showing that all convex polehedron graphs are 3-connected
Tutte tended to use somewhat different terminology from some other authors, and I don't know his definitions here. The now "standard" approach to Steinitz's Theorem: A graph is 3-polytopal if and only if it is 3-connected is described in the books of polytopes by Grünbaum and Ziegler. Their approach allows graphs to be 4 or 5-connected but also 3-connected. Some 3-connected graphs are not 4-connected or 5-connected. The only proof I know of that 3-polytopes are 3-connected uses a theorem of M. Balinksi that the graphs of d-polytopes are d-connected.
Mar
20
comment showing that all convex polehedron graphs are 3-connected
The edge-vertex graphs of some 3-dimensional convex polytopes are more than 3-connected. For example the regular icosahedron's graph is 5-connected. One approach to 3-connectedness is to say that every pair of distinct vertices u and v can be joined by at least 3 paths whose only vertices in common are u and v. On the icosahedron for any pair of distinct vertices there are 5 such paths so the icosahedron is 5-connected.