3,876 reputation
711
bio website york.cuny.edu/~malk
location New York, NY
age
visits member for 4 years, 1 month
seen Sep 12 at 19:06

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


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.
Mar
20
comment Proving the easy direction of Steinitz's theorem.
One approach to answering this is to use facts about graphs of (convex) d-polytopes when d is 3 or more.
Sep
29
comment Recommend an intro to binary embedding algorithm in Graph Theory
I don't understand what you mean by a "binary embedding of a tree." There are many papers about embedding binary trees into graphs. For example, embedding binary trees into d-dimensional hypercubes.