CS1112 Spring 2009 Project 1 due Thursday 1/29 at 11pm
You must work either on your own or with one partner. You may discuss background issues and general solution
strategies with others, but the project you submit must be the work of just you (and your partner). If you work with
a partner, you and your partner must first register as a group in CMS and then submit your work as a group.
Objectives
Completing this project will help you learn ab out Matlab scripts, assignment statements, if-else statements,
and some Matlab built-in functions. You will also start to explore Matlab graphics.
1 Archimedean Soccer Balls
Soccer balls come in three sizes:
Size Circumference Intended
(inches) Age Group
3 23-24 Less than 8
4 25-26 8 through 12
5 27-28 Older than 12
In this problem we offer a conjecture that explains the circumference values in relative terms. You will
examine the validity of the conjecture by writing and running a Matlab script.
Our conjecture requires an “ancient Greek” appreciation for solid geometry so we start with some facts. A
solid is a Platonic solid if each face is identical in size and shape. There are only five:
Solid Faces Face Shape
Tetrahedron 4 equilateral triangle
Cube 6 square
Octahedron 8 equilateral triangle
Dodecahedron 12 regular pentagon
Icosahedron 20 equilateral triangle
Key attributes of a given Platonic solid Pinclude its edge length E,inradius r,outradius R, surface area S,
and volume V. The inradius of Pis the distance from its center to the centroid of any face. It is the radius
of the largest sphere that fits inside P. The outradius of Pis the distance from its center to any vertex. It is
the radius of the smallest sphere that encloses P. Problem P1.1.5 in the text is concerned with the nesting
of Platonic solids and is worth reviewing. The great Johannes Kepler discovered that the radii associated
with the nesting
Octahedron ⊂Iscosahedron ⊂Dodecahedron ⊂Tetrahedron ⊂Cube
have the same ratios to one another (approximately) as the orbit radii of the six visible planets. Following
in the footsteps of Kepler, we will attempt to explain the ratios
Size 5 Circumference
Size 4 Circumerence and Size 4 Circumference
Size 3 Circumerence
not by nesting Platonic solids, but by nesting truncated iscosahedrons. A truncated iscosahedron has 32
regular polygon faces. Twenty are hexagons and twelve are pentagons. A soccer ball can be regarded as a
“puffed out” truncated iscosahedron:
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