blindmen6:
“A number of year ago, in a public debate on the subject [of the true significance of mathematical investigation], I said that I could imagine an alien encounter during which, in response to learning of our scientific theories, the aliens remark, “Oh, math. Yeah, we tried that for a while. At first it seemed promising, but ultimately it was a dead end. Here, let us show you how it really works.” . . . I don’t know how the aliens would actually finish the sentence, and with a broad enough definition of mathematics (e.g., logical deductions following from a set of assumptions), I’m not even sure what kind of answers wouldn’t amount to math.”
-Brian Greene in The Hidden Reality
The Hidden Reality on YouTube.
theincompletenesstheorem:
educatingearth:
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:D I’m so glad I found this!
themathkid:
In the 1950s, Solomon W. Golomb investigated the question: how few cells can you remove from an 8×8 square to exclude the shape of a given polyomino? His book Polyominoes shows minimal exclusions for all polyominoes up through order 5. Presented here are the minimal known exclusions of hexominoes from an 8×8 square. The solutions shown are not necessarily unique.
themathkid:
You either get it or you don’t. [TAUTOLOGY!]
matthen:
Bouncing balls in a circle gives one of the simplest systems to exhibit chaos, as was pointed out in a comment by Andrew Moylan. The animation above shows two balls which start off with almost exactly the same speed and location, but before long they are travelling along completely different trajectories. Such high sensitivity to the initial conditions defines chaos.
In this visualisation, each point in the circle is given a colour in a rainbow pattern. The animation shows at each time where a ball dropped at each point within the circle has ended up, by colouring that point appropriately. For example at the first frame, all the balls are stationary, and we see the rainbow pattern. Then as time progresses, the balls drop down and the pattern correspondingly goes up. A black band appears and moves up, which shows which balls are doing their first bounce. Soon the order disappears- it looks random like the divergence of the two balls above. [more] [code]
themathkid:
symmetricalstars:
themathkid:
The Catalan numbers give the number of ways to tile an n-sized stair case with exactly n rectangles.
That’s so interesting!
Continuing on my previous post:
The 42 tilings here also represent the Catalan number C7. Surely there is a bijection from these tilings to the heptagon triangle dissections [see previous post]. Help me find it?
— Bharati Krishna Tirthaji (via mathstalio)
thatmathblog:
This is the Rhind Papyrus — and 18 foot long scroll which carries Egyptian problems pertaining to fractions, numeric patterns, surveying, etc. Written by the scribe Ahmes in roughly 1650 BC, it uses the earliest-discovered notation for a mathematical operation: addition is denoted by a pair of walking legs! (such as 2 *walking legs* 2 is 4)