@enumerator hi

@enumerator can I interest you in 1, 2, and 076?

@enumerator hi

Another unicode mystery: the Unicode character ℇ, U+2107, is labelled "EULER CONSTANT", but nobody can work out what it's supposed to stand for. The base of the natural logarithm is normally written as 'e', and the Euler-Mascheroni constant is normally written as 'γ'.

A 2002 post on the Unicode mailing list seems to basically say it's a mistake: http://unicode.org/mail-arch/unicode-ml/y2002-m04/0073.html

of course, the nanomb2 algorithm (aka "super series approximation") does work sometimes, and when it does it is often much faster than the older series approximation algorithm, which in turn is much faster than perturbation iterations alone, which in turn is much faster than using plain iteration with high precision numbers for each pixel

the algorithm works by approximating the orbit near a periodic cycle (usually a minibrot island) by a polynomial in *two* variables representing small changes in C and Z. you end up with a polynomial that does P iterations at once (a "super iteration"), where P is the period of the cycle.

this polynomial is only valid while dC and dZ are small, but when they get big you can switch to a different polynomial corresponding to a nearby less zoomed in minibrot of lower period. one "super-iteration" takes longer than one perturbation iteration or one plain iteration, but you need far fewer, so it works out faster.

combined with interior checking, you can set the iteration count exceedingly high (100100100 is routine for me now) with little-to-no slowdown, and get super-crisp minibrot boundaries

150. DISSECTING A MITRE. The figure that is perplexing the carpenter in the illustration represents a mitre. It will be seen that its proportions are those of a square with one quarter removed. The puzzle is to cut it into five pieces that will fit together and form a perfect square. I show an attempt, published in America, to perform the feat in four pieces, based on what is known as the "step principle," but it is a fallacy.

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If I ask you to "decompose a fraction into partial fractions", what should you do?

Warning: I'm looking for edge cases and loopholes.

#math

Wow, the statistical concept of #variance turned 100 years old this July. That's so young in the mathematical history scale! It's hard for me to imagine statistics without variance.

What a treat! Over the weekend I received an unexpected email from a fan, containing proofs of the Riemann hypothesis, Fermat's last theorem, the Beal conjecture *and* the abc conjecture! Furthermore, they're all proved by the one proof! #blessed

Inspired by an article in @chalkdustmag, I wrote code to generate Truchet tiles for any even number of sides. Then I looked up which tilings of even-sided polygons exist, and here we are: http://somethingorotherwhatever.com/truchet-polygons/

I'm looking in A-Level #math textbooks for examples of "simplification".

On the first page of content in this EdExcel C1 book, this made me so cross: you're not applying the rule \((a^m)^n = a^{mn}\), you first need \((ab)^n = a^n b^n\), but that rule isn't even listed!

Prompted by @11011110, I've had a go at making a Mathstodon emojo:

It's a 𝕄 with an elephant's trunk. Helpful suggestions for my colourblind eyes welcome!

@christianp The space before the \(dx\) in an integral (unless you’re picky and write \(\text{d}x\)).

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