#standupmaths

[bernie-buddy]

A 3D volumetric rendering of a 4D rendered torus, often referred to as the "Tiger", due to its exotic shape.

The same image in 2D slices:

[mejaydee]

Me spending money on hobbies I’m obsessing over but will never actually participate in

[mathblab]

Mathematicians don’t like math because it’s easy, they like math because they enjoy how hard it is.

— Matt Parker (paraphrased)

[adventures-in-asexuality]

This is fascinating and charming. Discover a new shape, the importance of interdisciplinary collaboration, and how to occupy yourself while in a strange city!

[lilacchao]

matt parker just released an excellent video about number divisibility rules that has made me realise just how gorgeous divisibility rules are in base 6 (discussed under the cut)

every number in base 6 that doesn't end with 1 or 5 is divisible by 2 or 3, so to come up with a divisibility rule for some number 'n':

. divide 'n' by 10, 2, and 3 as much as possible (10 while it ends with 0, 2 while it ends with 2/4, 3 while it ends with 3) so it now ends with 1 or 5, call the result 'a', and call the product of all those 6s 2s and 3s 'b'

. (note that dividing by 2 or 3 is easy in base 6, just triple or double respectively and remove a zero - eg, 32/2 = 160/10 = 16, 15/3 = 30/10 = 3)

. split 'a' into two numbers, 'a1' (all but the last digit) and 'a2' (the last digit)

. if 'a2' is 1, the divisibility rule for 'a' is "take off the last digit of the number, multiply it by 'a1', and subtract it from the rest, and repeat until you get to a number small enough to recognise from multiplication tables"

. if 'a2' is 5, the divisibility rule for 'a' is "take off the last digit of the number, multiply it by 'a1', and add it to the rest, etc"

. split 'b' into two factors: all but the trailing zeroes, which is gonna be either 2^x or 3^x for some 'x', and 1 followed by all the trailing zeroes, which is equivalently 10^y for some 'y'

. given 2^x, define 'c' as 3^x, given 3^x, define 'c' as 2^x

. the divisibility rule for 'b' is to first multiply by 'c' then check if it ends with at least x+y zeroes

. the divisibility rule for 'n' is to do the divisibility rules for both 'a' and 'b', and if it's divisible by both 'a' and 'b', it's divisible by 'n'

example: is 11003535 divisible by 1220?

1220 = 41×20, so a=41, a1=4, a2=1, c=3, x=1, y=1

test for divisibility by 'b': 3×11003535 = 33015453, nope we wanted two zeroes and we found none, sad!

unnecessary now, but test for divisibility by 'a': 11003535 -> 1100353 - 4×5 = 1100321 -> 110032 - 4×1 = 110024 -> 11002 - 4×4 = 15534 -> 1553 - 4×4 = 1525 -> 152 - 4×5 = 120 -> 12, nope, 12 clearly isn't a multiple of 41

this is all a bit much to do in your head, but with basic familiarity with base 6, really easy on paper (or on phone like me just now!), and the divisibility rules are so easy to figure out!

[sailormaya]

happy pi day it's a perfect day to watch matt parker find amongi in the digits of pi

[dancing-out-my-pants]

Today is the day, the most palindromic day. To learn why watch standupmaths' video on it, it's worth a watch.

[everythingispermited]