Math Snippets

The sphere is “inscribed” in the cylinder. It’s north pole just touches the top of the cylinder; the south pole just touches the bottom. And the cylinder and sphere just barely make contact all along the equator. If the cylinder were the least bit shorter or skinnier, the sphere would not fit inside.If r = …more about Archimedes Tombstone

The symbol, , has been around for more than two thousand years. The Romans used it to represent 1000, a BIG number to them.About 1650 the English mathematician, John Wallis, proposed that stand for INFINITY, and that stuck. The concept of infinity has tantalized and sometimes troubled mankind even longer. Zeno of Elea (495 BC?-425 …more about Counting to Infinity

Soap films and soap bubbles are examples of “minimal surfaces,” so-called because nature selects the shape that requires the least amount of total energy to maintain, and thus enclose a given area/volume with as little perimeter/surface area as possible. (A circle takes the least perimeter to surround a given amount of area; and a sphere …more about Plateau’s Problem

Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in southern Italy. Pythagoras was a teacher, a philosopher, a mystic and, to his followers, almost a god. His thinking about mathematics and life was riddled with …more about Pythagorean Theorem

1. Start with a long rectangle (ABCD) made of paper. 2. Give the rectangle a half twist.3. Join the ends so that A is matched with D and B is matched with C. This curious surface is called a Möbius Strip or Möbius Band, named after August Ferdinand Möbius, a nineteenth century German mathematician and …more about The Möbius Strip

Start with an equilateral triangle whose sides have length 1.On the middle third of each of the three sides, build an equilateral triangle with sides of length 1/3. Erase the base of each of the three new triangles.On the middle third of each of the twelve sides, build an equilateral triangle with sides of length …more about The Snowflake Curve

Selected References Books Spatial Tessellations: Concepts and Applications of Voronoi Diagrams by Okabe, Boots and Sugihara, John Wiley & Sons, 1992. This is the bible. Definitions, properties, algorithms, generalizations and applications galore! Unfortunately, it retails for $180. The King County Library System has one copy. There are several copies scattered among academic libraries in the …more about Voronoi Diagrams