all notes filed under mathematics • random notes, links and pixels • dullneon.com

Repeat after me and you’ll be fine.

Yes, talking about binomials and (a + b)² is all rather elementary, but it’s never too late to revisit the foundations that make the simple stuff simple.

Tags:

binomial, simple, square

Everything you know about √ is wrong.

Tags:

division, funny, square root, symbol

An illustrated guide to the Advanced Encryption Standard.

Tags:

AES, comic, computing, cryptography, draw, encryption, funny

Love is like Pi.

Some great work from Andrew Le. Show some irrational love to him, will you?

Tags:

funny, pi, poster

A 30 digit piem.

Sir, I send a rhyme excelling,
In sacred truth and rigid spelling,
Numerical sprites elucidate,
For me the lexicon’s dull weight,
If nature gain, not you complain
Tho’ Dr Johnson fulminate.

›› A nice Piphilology for 3.141592653589793238462643383279

Tags:

mnemonic, pi, piem, piphilology

Formula for the volume of a pizza.

Let’s say we have a pizza. It has a radius of z and it has a height of a. That would mean it has a volume of

pi * z * z * a.

Thank you reddit. (And yeah, my computer science background makes me define this as a formula, not an algorithm.)

Damn, I’m hungry.

Tags:

algorithm, circle, formula, pizza, reddit, volume

Should have started with 33 tortilla chips.

Tags:

fibonacci, nachos, nerd, numbers, tortilla chips

Kaprekar’s constant.

Take any four-digit number whose digits are not all identical.
(Let’s take 3141 as an example.)
Rearrange the string of digits to form the largest and smallest four digit numbers possible, padding it with leading zeroes if needed.
(We get 4311 as the largest number possible and 1134 as the smallest.)
Subtract the smaller number from the larger one.
(4311-1134 gives us 3177.)
With the result, repeat step 2 above.
(7731 - 1377 = 6354, 6543 - 3456 = 3087, 8730 - 0378 = 8352, 8532 - 2358 = 6174, 7641 - 1467 = 6174)

Within about seven steps, you’ll hit the number 6174. This works for any four digit number that doesn’t have repeated digits (like 8888 which will immediately give a zero after step 2). The magic number for three digit numbers is 495. This remarkable phenomenon was discovered by D. R. Kaprekar in 1949.

Tags:

495, 6174, digit, formula, india, numbers

Thursday, 11th September 2008

Nomograms.

Before the days of calculators and computers, Nomograms (or Nomographs) were often used to approximately calculate values of a function. There are specific nomographs for specific applications and all of them will only give approximate answers (since accuracy is dependent on the precision of the drawing itself). Invented by French mathematicians Massau and M. P. Ocagne in 1889, the precision, geometry and symmetry involved in the graphics of Nomography can produce some beautiful ‘visualizations’ like the Smith Chart above.