Love this proof my liberal arts students found for 1+2+3+4+3+2+1=4^2. (Count the squares vertically.) 
- Steven Strogatz  @stevenstrogatz  Oct 16

Love this proof my liberal arts students found for 1+2+3+4+3+2+1=4^2. (Count the squares vertically.)

- Steven Strogatz  @stevenstrogatz  Oct 16

ryanandmath:

Can you tell which plot above is randomly generated?

Being able to determine if something is “truly” random is not just an investigation carried out by forensic accountants, sociologists, and law enforcement. Rather it is an interesting and complicated mathematical problem. Consider the two plots above. You may look at the on the left and see the clumps, the spacing, and think “That can’t be the random plot.” And yet it is. The plot on the left has been randomly generated, while the plot on the left is a scatter plot of glowworm positions on a ceiling.

So here, the clumps actually help indicate randomness. Try thinking of it in another way: imagine you have two students who were asked to flip a coin 100 times for homework. The first student was diligent and flipped accordingly:

THHHTHTTTTHTTHTTTHHTHTTHT
HHHTHTHHTHTTHHTTTTHTTTHTH
TTHHTTTTTTTTHTHHHHHTHTHTH
THTHTHHHHHTHHTTTTTHTTHHTH

The second student was lazy and decided to make up his flips:

HTTHTTHTHHTTHTHTHTTHHTHTT
HTTHHHTTHTTHTHTHTHHTTHTTH
THTHTHTHHHTTHTHTHTHHTHTTT
HTHHTHTHTHTHHTTHTHTHTTHHT

Now while it might seem strange that the first student has long runs, it fits closer to what one would expect if the flip is random. On the other hand, in the second student’s data, there is less than a 0.1% chance that they wouldn’t get a single run longer than four in a row!

The images and coin flip data was found at this article. It takes a closer look at some of these topics and provides some pretty neat historical background.

Coffee cup joke

curiosamathematica:

A topologist is drinking coffee from a cup. Suddenly the handle drops off, leaving the topologist in astonishment: the new shape is different, but he can still drink from it! So he keeps on drinking his coffee, until the bottom of the cup drops off. Now he is totally befuddled: the shape is equivalent to the original one, but how can he drink his coffee now?

“It is impossible to be a mathematician without being a poet in soul.”

— Sofia Kovalevskaya

arcymonek:

matematyka niepodzielnie rządzi :)

Mathematics and sex: Clio Cresswell at TEDxSydney 2014 “Mathematics and sex are deeply intertwined. From using mathematics to reveal patterns in our sex lives, to using sex to prime our brain for certain types of problems, to understanding them both in terms of the evolutionary roots of our brain, Dr Clio Cresswell shares her insight into it all.”

matthen:

Unrolling these circles gives fills a triangle with base 2 π r and height r (where r is the radius of the filled disk). Such a triangle has area π r2. This does not serve as a complete proof for why this is the area of a circle, but can give you some intuition for why it should be. [code]

matthen:

Unrolling these circles gives fills a triangle with base 2 π r and height r (where r is the radius of the filled disk). Such a triangle has area π r2. This does not serve as a complete proof for why this is the area of a circle, but can give you some intuition for why it should be. [code]

Genaille-Lucas Rulers
One of the shitty things about all the technology and computing power we have access to in this day and age is that awesome tools like these Genaille-Lucas rulers are redundant.  

Genaille-Lucas Rulers

One of the shitty things about all the technology and computing power we have access to in this day and age is that awesome tools like these Genaille-Lucas rulers are redundant.  

New re-worked logo to celebrate Mindfuck Math’s one year anniversary!

New re-worked logo to celebrate Mindfuck Math’s one year anniversary!