Visualizing mathematics

by | Wednesday, August 27, 2008

I love visual proofs of mathematical theorems. One visual proof I use quite often in my design courses (CEP817 or CEP917) is a visual proof of the fact that the sum of consecutive odd numbers is a square number.

In other words:

1 + 3 = 4 = 22

1 + 3 + 5 = 9 = 32

1 + 3 + 5 + 7 = 16 = 42

… and so on.

Mathematically speaking that translates to

1 + 3 + … + (2N-1) = N2

Now one can go about proving this fact this through algebra OR one could just do it visually. Check out this image below,

… or better still go to this applet

Pretty cool huh?

Looking for the above applet led me to this other cool visual proof for

(a + 1)2 = a2 + 2a + 1

Check it out.

A few randomly selected blog posts…

Pi(e) day, 2019

Pi(e) day, 2019

A design created in celebration of Pi-day, 2019. (More context about the day here and more about the number itself here). As always, the OofSI team celebrates Pi(e) day by offering a selection of Pi(e)'s - exactly at 1:59 PM. Totally irrational I know! Apart from...

Better late than never, 21st century learning

Better late than never, 21st century learning

Quest Alliance is an NGO based in Bangalore that seeks to equip young people with 21st century skills by enabling self-learning. I have known of Quest and its director, Aakash Sethi, for over a decade now. In fact I had blogged about Quest back in 2008 here, and...

Bollywood meets Guitar Hero

Over the Christmas break my daughter and three of her friends got together to make a music video. The idea was simple, what if there were a version of Guita Hero (Sitar Hero anyone?) for Bollywood songs. Out of this idea emerged a 5+ minute long music video - with a...

The future of work & learning: An interview

The future of work & learning: An interview

I had posted earlier about my visit to Bangalore back in summer to participate in the Quest 2 Learn Annual Summit organized by the Quest Alliance. The two day conference focused on The future of work and learning. During my visit I was interviewed by Aakash Sethi, the...

Happy Valentine’s Day: Old/New ambigram

Happy Valentine’s Day: Old/New ambigram

I had made this design a while back, just hadn't posted it online. (Actually a hand-drawn version is on this website somewhere.) Have a great day, everyone!

Chinese-English Ambigrams

During my travel through Taiwan and Hong Kong, I usually opened my presentations with some bilingual ambigrams - words that can be read in Chinese AND English. These ambigrams were created by David Moser, someone I got to know, virtually, through Doug Hofstadter's...

Shin, et. al. wins Outstanding paper award

Just found out that Shin, T., Koehler, M.J., Mishra, P. Schmidt, D., Baran, E., & Thompson, A.,(2009, March). Changing technological pedagogical content knowledge (tpack) through course experiences. Paper presented at the 2009 International Conference of the Society...

1 Comment

Submit a Comment

Your email address will not be published. Required fields are marked *