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Vertex Configurations: Platonic Solids, Archimedean Solids, and Johnson Solids

Last week, we explored the world of Euler’s Formula: the relationship between Vertices + Faces — Edges = 2 in any convex polygon. The children were tasked to find polyhedra (solids) in their home and test for vertices, faces and edges. If the solid was concave, Euler’s Formula doesn’t necessarily work.

Euler’s Theorem Convex Polyhedra Vertices + Faces — Edges = 2

While studying building solids with triangles, rectangles, pentagons, and hexagons, I tried to follow the Four Color Map Theorem and found that it worked for convex polyhedra. What is polyhedra? A polyhedron is a solid with flat faces (poly means many, and hedron means faces).

Four Color Map Theorem Creates New Branch of Mathematics: Graph Theory

Francis Guthrie, a 21 year old mathematics student at University College in London, was mapping the counties of England in 1852 when he noticed that he only needed four colors for the map. 

Adjacent Borders, Countries with Most, All US States, Mean and Mean Absolute Deviation

LIST THE NUMBER OF US STATES ADJACENT TO EACH US STATE (circle the number)

 

Sports Field/Court/Rink Dimensions -- Architectural Drawings To Scale

After last week exploring the Major League Baseball Fields Dimensions, Outfield Square Footage and Homerun Distance, I received a lot of interest from the students to look at other sports fields dimensions.