# Featured

## Volume and surface area of Human Body, World Population of Living Matter

When doctors see patients, they almost always take two measurements first: height and weight. Yes, they want to track their patient’s progress but more importantly, they need to understand the patient’s volume and surface area for prescribing medicine.

## Volume of Rectangular Prisms, Cubes, and Platonic and Archimedean Solids

Every student is taught the formulas for the volume of a rectangular prism as length times width times height, the three dimensions of a rectangular prism. The answer must be give in cubic units.

## 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.