Lecture 10

Platonic Solids and Conic Sections

1. Artists from the renaissance :

(a) Polyhedra, Luca Pacioli 1445-1514

(b) Intarsia Polyhedra , Fra Giovanni c.1520

(c) Geometria et Perspectiva 4, Lorenz Stoer, 1567

2. The ubiquitous Escher:

(a) Do you recall the reptiles ?

(b) A tetrahedron (Tetrahedral Planetoid, 1954)

(c) A double tetrahedron (Double Planet, 1949)

(d) Find Waldo (Stars, 1947)

3. A script with all of the regular solids (as interactive 3D graphics) and many other polyhedra is accessible through the webMath page for this course.

5. Generic conic sections:

(a) circle

(b) ellipse

(c) parabola

(c) hyperbola

4. Here is the standard string-art picture of a parabola.

Two such parabola and ... an "eye". Here are a bunch of parabolas in a cuter picture.

5. Playing with a cardoid: a script for constructing hearts with strings.

© Sasho Kalajdzievski