Mihai Caragiu - NOTES ON THE NINE POINT CIRCLE, THE SIMSON LINE AND RELATED TOPICS (Mathematics Bonus Files - April 17, 2009). ABSTRACT: These notes are based on the proofs of the nine point circle and the Simson line theorems prepared by the author for the 2006 and 2007 Summer Honors Institute camps held at the Ohio Northern University, and on the author’s 2007 October 26 talk presented at the Ohio MAA Fall Meeting held at Wittenberg University.

## Saturday, June 27, 2009

## Tuesday, June 16, 2009

### "A New Online Computation Engine..."

From the Wall Street Journal, June 16, 2009 - an article by Carl Bialik on Wolfram|Alpha -

A New Online Computation Engine Shakes Up Math

A New Online Computation Engine Shakes Up Math

## Monday, June 8, 2009

### Giovanni Domenico Cassini (1625–1712)

Giovanni Domenico Cassini was born on June 8, 1625. He investigated the curves that are now known as the Cassini ovals defined by equations of the form

where

*q*

_{1 }and

*q*

_{2}are fixed points, "dist" is the Euclidean distance in the plane, and b is a constant. The above picture displays a few Cassini ovals, with foci

*q*

_{1}(-1, 0) and

*q*

_{2}(1, 0), annotated with the value of

*b*

^{2}.

In 1680, while director of the Paris Observatory he discovered the identity

satisfied by the Fibonacci numbers. This is now known as the Cassini identity. A quick proof by using determinants:

A bijective proof was provided by M. Werman and D. Zeilberger - "A bijective proof of Cassini's Fibonacci identity", Discrete Mathematics 58 (1), 109 (1986).

Also see the Cassini biography from MacTutor.

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