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Then you should say what you mean, the March Hare went on.
"I do, " Alice hastily replied; "at least I mean what I say, that's the same thing, you know."
"Not the same thing a bit!" said the Hatter. "Why, you might just as well say that "I see what I eat" is the same thing as "I eat what I see!"
Alice in Wonderland.
Loci: Convergence
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Mathematical Treasures
Johann Kepler's Uralten Messekunst Archimedes
Johannes Kepler ( 1571—1630 ) was concerned that Austrian wine merchants were cheating their customers by gauging the volume of their barrels incorrectly. To correct the situation, he undertook a study of the volume of wine barrels. He published his findings, Nova Stereometria Doliorum vinarorum, in 1615. Forsaking classical techniques of volume calculation, Kepler produced solids of revolution, dissected them into an infinite number of circular laminae and obtained a volume summation. He applied this technique to consider solids other than wine barrels; in total studying the volumes of 92 different solids. Written in Latin this work was scholarly and had a limited audience. In order to increase his financial returns in 1616, he published a popular German language version of his work, Ausszag aus der Uralten Messekunst Archimedes. The page images are from the Messekunst. Page 27 contains a discussion on the volume of a torus. Page 28 returns to a consideration of the volume of wine barrels.
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THe first to say
THis is a great article that helped me with a class I have. I loved geting to see what the book looks like-it is facinating.
thread #2:
Looking for a video about peaks, valleys, ridges
I once saw a very interesting video describing the mathematics of peaks, valleys, and ridges with a result like Euler's formula for Polyhedra. I think it was by Milner. Could you help me locate it?