Jenn3D

Posted on September 7, 2011 by daniela2daniela

We start the software-of-the-week series with Jenn3D. I don’t know what Jenn stands for, but my children say it has to do with “genial”. It’s a free program for Win and Mac; sources are available and can be compiled for other platforms. Look it up at http://www.math.cmu.edu/~fho/jenn/#download

The program presents a wide variety of regular and semiregular polytopes, that get to be embedded into the 3-sphere and stereographically projected on the affine 3-space. The resulting 3D object can be “ordinarily” manipulated inside the screen. To fully understand the program, it’s best to have an idea of conformal mapping in 2D and 3D, and an intuitive notion (if not a formal one) of projective plane and projective 3-space, but it’s really enjoyable by anybody, even supposed math-haters. Yes, it was tested by our team under the severest conditions.

The Shape of Space

Posted on September 7, 2011 by daniela2daniela

I think the “book of the week” column has to start with a book by Jeff Weeks 🙂

We are going to talk here about an awesome book, The Shape of Space, and a dull book, Exploring the shape of space, a dumbed version for schools. Why schools have to be stupid places, it beats me, but anyway. In any case, get the dumb book and grab the included CD (not sold separately) for a great video interview, including Macs before OS X, and for some applets on multiconnected spaces. You can also, since you are at it, try out the nicest “activity”: design 2D living beings. Then, it’s time to study the real book.

The Shape of Space is by far the best resource for multiconnected spaces at elementary level. Nothing is taken for granted, the book even explains what a Klein bottle is. Including exercises of all sorts. Quit wasting time reading this review, and open the book. Super-recommended for anyone who can read: illitterate friends, get someone to read this to you.

Two peasant ladies go to the market

Posted on September 6, 2011 by daniela2daniela

It looks like nobody wants to be the first one to publish a post!

I’ll do, but the first post won’t be mine either. This is a problem I read somewhere in a book or article by V. I. Arnol’d.

Two peasant ladies leave simultaneously at dawn because they are going to a farmers’ country market: one lady leaves from town A and is going to B, while the other one is on her way from B to A. They walk at constant speed (each one at her own speed). At midday sharp, they greet each others without stopping and continue on their way.

At 16 (that is, 4 p.m.) the faster lady reaches her destination, and at 21 the other lady arrives, too.

Compute sunrise time.

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