In about 300 BC Euclid developed a geometrical approach which, although later mathematicians used it to solve quadratic equations, amounted to finding a length which in our notation was the root of a quadratic equation. Euclid had no notion of equations or coefficients but worked with purely geometrical quantities. ... The treatise develops a system for the solutions of quadratic expressions including geometric principles for completing the square. ... The geometrical part of Pacioli's Summa is discussed in detail by Glushkova and Glushkov. The authors write: The geometrical part of L...

• Word Count: 1938
• Approx Pages: 8

Oral instructions were given in geometric terms. ... Patience, precision, "don't give up-, creativity, geometric concepts, and that math class is fun. ... If we build a polyhedron then, sure, we encounter a shape from geometry. ... On this page, you will find instructions for making a "Magic Pinwheel", an amazing model by Robert Neale that slides from a pinwheel shape to an octagonal ring and back again. ...

• Word Count: 1525
• Approx Pages: 6
• Has Bibliography

The lectures he attended and friendships he developed in GÖttingen would shape Dedekind's future endeavors. ... In 1821, French mathematician Cauchy began to clarify the basis of calculus with his theory of limits, a purely arithmetic theory that did not depend on geometric intuition or infinitesimals. ... The primary motivation behind part one of his book, Continuity and Irrational Numbers, was the desire to replace loose geometrical concepts and intuitive justifications with exact proofs stemming from precisely formulated definitions. ... But the important difference here is that...

• Word Count: 2467
• Approx Pages: 10
• Has Bibliography
• Grade Level: Undergraduate

"The patterns strategy requires students to examine sequences of numbers or geometrical objects in search of some rule that will allow them to extend the sequence indefinitely." ... Spatial ability is the ability to see and understand the relationships between shapes, spaces, or areas. This area can be noticed in the child's early years as they play with toys dealing with shapes and placing. ...

• Word Count: 2252
• Approx Pages: 9
• Grade Level: High School