Archive for the ‘Algebra’ Category

Math cheat sheets on the web

Friday, February 22nd, 2008

While surfing the web I discovered this very cool 10 page Math cheat sheet! document.write(''); Read this doc on Scribd: Math cheat sheet - by Dr Seiden var scribd_doc = new scribd.Document(4549, '1tws15et2yl5j'); scribd_doc.write('embedded_flash_4549_7fgxe'); You can download the PDF file here. Scoring this gem led ...

Trachtenberg speed multiplication: exploring why it works

Friday, February 15th, 2008

Last November I wrote about the Trachtenberg system of speed mathematics and showed one of the techniques - multiplying an arbitrarily large number by 12 with great ease. In this article I want to show you why the technique for multiplying by 12 works, share two more of the Trachtenberg ...

Interesting little Math problem

Friday, February 8th, 2008

Here's an interesting little problem. I made this one up but I bet it's been thought of by students of number theory and diophantine equations in particular. Let's say you have two kinds of postage stamps, one with a value of 3 cents, the other with a value of 5 cents. ...

Math magic with the number 9

Friday, February 1st, 2008

9 is a most interesting number. I'm sure that's largely because 9 is 1 less than 10 and most of us have 10 fingers (or digits) and we do arithmetic in a base 10 system. I've seen an amazing number of math tricks that take advantage of something called ...

How does Arthur Benjamin square 5 digit numbers in his head?

Wednesday, January 30th, 2008

Last month I blogged about mathemagician Arthur Benjamin and his amazing mental Math feats. Benjamin is a master of doing arithmetic in his head with lots of digits involved. In particular, he's able to square a 5-digit number without writing down partial results. How does he do it? I picked ...

Five constants tie together multiple branches of mathematics

Tuesday, January 22nd, 2008

I imagine that many of you are familiar with this remarkable mathematical equation that incorporates what are arguably the five most important mathematical constants into one equation. Yes, phi is missing from this equation. I've been reading this fascinating book, Where Mathematics Comes From. Wikipedia has an article about the ...

Vedic multiplication using bases: an introduction

Saturday, January 12th, 2008

There are numerous introductions to Vedic mathematics on the web. I won't be doing a general introduction to Vedic Math now. In this article I want to explore one particular Vedic mathematics technique, using something called bases, to optimize certain multiplication problems. This technique is extremely powerful and it takes getting ...

12 days of Christmas: an exploration in counting presents

Monday, December 24th, 2007

A popular winter Math problem is the counting of presents given during the 12 days of Christmas. On the 1st day of Christmas my true love gave to me a partridge in a pear tree. On the 2nd day of Christmas my true love gave to me 2 turtle doves, and ...

Mathcast #4: Quick squaring of 2-digit numbers

Monday, December 10th, 2007

Here's a video on how to quickly square a 2-digit number. The technique is based on this algebra: If you have a number with digits "ab" then the number is 10a+b. (10a+b)^2 = 100a^2+20ab+b^2. If you enjoy this video check out all of the Wild About Math! mathcasts. [youtube]http://www.youtube.com/watch?v=_wjxgz6r-_U[/youtube] SHARETHIS.addEntry({ title: "Mathcast #4: Quick squaring ...

The algebra of cross-multiplication

Thursday, December 6th, 2007

A few people were underwhelmed with my video on how to multiply together a pair of 2-digit numbers without writing down partial results. They didn't see a time savings. Fair enough, although not needing to write anything but the three (or four) digits of the answer can be a nice ...