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updated version is published in Mathematical Intelligencer, Vol. 23, No. 2, pp. 17-28, Spring 2001. David W. Henderson Department of Mathematics, Cornell University, Ithaca, NY, USA, dwh2@cornell.edu Daina Taimiða Department of Mathematics, Cornell University, dtaimina@math.cornell.edu For God's sake, please give it up. Wolfgang Bolyai urging his son János Bolyai to give up work on hyperbolic geometry. In June of 1997, Daina was in a workshop watching the leader of the workshop, David, helping the participants study ideas of hyperbolic geometry using a paper and tape surface in much the same way that one can study ideas of spherical geometry by using the surface of a physical ball. But, Wait! Constructions of Hyperbolic Planes We will describe three different isometric constructions of the hyperbolic plane (or approximations to the hyperbolic plane) as surfaces in 3-space. 1. This is the paper and tape surface that David learned from William Thruston. Figure 1. 2. Figure 2. Figure 3. 3. 1.

Math Isn't Just Computation. So Why Is That All We Teach? - Education \n A reader named Monika Hardy recently noticed that I harp a lot on the importance of math when blogging about education. (Guilty as charged.) So, she sent me an excellent talk from the recent TEDGlobal event from this summer. The elements of math, according to Wolfram are: posing questions, translating real world problems into mathematical language, performing computation, and translating mathematical answers into real world solutions. Computers should be doing those calculations. What about the processes needed to solve mathematical problems? Check out the video, it's really good stuff—at least, I think so. \n A reader named Monika Hardy recently noticed that I harp a lot on the importance of math when blogging about education. The elements of math, according to Wolfram are: posing questions, translating real world problems into mathematical language, performing computation, and translating mathematical answers into real world solutions. Computers should be doing those calculations.

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