Suggested Reading: The Simpsons and their Mathematical Secrets

June 8, 2014

Simon Singh — The Simpsons and Their Mathematical Secrets — Bloomsbury, 2013, 255 pp. ISBN 978-1-62040-277-1

(Buy at Amazon.com)

(Buy at Amazon.com)

Using, as an excuse, the fact that The Simpsons (and their sister series Futurama) use mathematics as part of the plot or as a “frame freeze gag” (a gag that is so short that unless you look at the show frame by frame, you might miss it), Singh (which you may remember from books such as The Code Book and Fermat’s Last Theorem) brings us along a mathematical walk, presenting us the mathematically-inclined writers of the shows. But, as I said, The Simpsons are merely a convenient excuse to introduce mathematics and theorems: if you expect to learn a lot about The Simpsons themselves, you’d be disappointed. The book is about the mathematics and the writers.

However, it’s an interesting read: prime numbers, \pi, combinatorics, computation and algorithmics. I especially liked the Futurama Theorem that describes how, using a mind-swapping machine that can swap minds between two same individuals once only, we can un-scramble minds and bodies and put every one in their rightful body (not a new plot device, Stargate did it first, in s02e18).


Suggested Reading: How Mathematics Happened: The First 50000 Years

May 19, 2014

Peter S. Rudman — How Mathematics Happened: The First 50000 Years — Prometheus Books, 2006, 314 pp. ISBN 978-1-59102-477-4

(Buy at Amazon.com)

(Buy at Amazon.com)

What first got me interested in this book is the “50000 years” part. I was preparing lectures notes for my course on discrete mathematics and I wanted my students to have an idea of what prehistoric maths might have been, say, 20000 years ago. Unfortunately, you wont learn much about this in this book

The book does hint about what mathematics might have been in hunter-gatherer times, and how it might have affected later developments. But that lasts for about a chapter or so, and the remainder is devoted to historical mathematics: Ancient Egyptian, Babylonian, and Classical Greek. All kinds of numerical algorithms are covered, presented in great detail, making the book more technical than historical. Some part are speculative as the historical record is incomplete at best, but it is speculative in the best way possible, with every assumption backed by an actual historical observation.


Closed for Summer (2014)

May 13, 2014

I have been absurdly busy lately and I cannot keep with the pace of posting one new post per week. Now that the semester’s over, I must take advantage of the few blessed months of summer to further my research, and the blog isn’t top priority. But, rest assured, I will be back in september to resume the once-a-week post schedule.

Until then, enjoy your summer.

PICT0212-crop


Blasons, Poésies Anciennes (Ebook, DjVu)

May 13, 2014

M. D. M. M*** — Blasons, Poésies anciennes des XV et XVImes Siècles, extraites de différens auteurs imprimés et manuscrits, nouvelle édition, augmentée d’un glossaire des mors hors d’usage — Paris, Gillemot et Nicolle, 1809

blasons-1809

This book was scanned with the help of Christine Arsenault at the Centre Joseph Charles Taché, a research center on the literary history of Canada.


Yet Another Square Root Algorithm (part II)

May 6, 2014

last week, we saw that we could use a (supposed) efficient machine-specific instruction to derive good bounds (but not very tight) to help binary search-based and Newton-based square root extraction algorithms go faster. Last week, we saw that the technique did lead to fewer iterations in both algorithms.

malevich-square

Now, does the reduced number of iterations translate into actual, machine speed-up?

Read the rest of this entry »


Yet another Square Root Algorithm

April 29, 2014

Computing (integer) square root is usually done by using a float square root routine and casting it to an integer, possibly with rounding. What if, for some reason, we can’t use floats? What are the possibilities?

malevich-square

One possibility is to use binary search to find the square root of a number. It may be a good choice because it will only perform a number of iterations that is half of the (maximum) numbers of bits of the number (we will explain why in a moment). Another possibility is to use Newton’s method to find the square root. It does a bit better than binary search, but not exceedingly so: on very small integers, it may iterate a third as much iterations as binary search, but on large integers, it will do only a bit fewer iterations. Can we do better? Yes!

Read the rest of this entry »


Count Like an Egyptian (Part II)

April 22, 2014

In a previous entry, we discussed egyptian fractions and, in particular, a greedy algorithm to convert them. We noticed that, once in a while, the greedy algorithm generates a really large denominator, despite harmless-looking fractions:

\displaystyle \frac{412}{1000}=\frac{1}{3}+\frac{1}{13}+\frac{1}{574}+\frac{1}{699563}

So, I had an idea to, maybe, minimize the size of the maximum denominator.

Read the rest of this entry »


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