Pinned toot

Hallo, new Mastodon users! Here on mathstodon.xyz we've got a couple of mathematical emoji: and . I'd love to add some more. If you can make a PNG image the same size as those, send it to me and I'll add it. Faces of famous mathematicians are an easy place to start; could we have some shapes, polyhedra, or other mathographics too?

A problem of mine appeared in the lastest Mathematics Magazine:
Suppose $$\pi$$ is a permutation of $$\{1,2,\ldots,2m\}$$. Consider the (possibly empty) subsequence of $$\pi(m+1),\pi(m+2),\ldots,\pi(2m)$$ consisting of only those values which exceed $$\max\{\pi(1),\ldots,\pi(m)\}$$.

Let $$P(m)$$ denote the probability that this subsequence never decreases, when $$\pi$$ is a randomly chosen permutation of $$\{1,2,\ldots,2m\}$$. Evaluate the limit of $$P(m)$$ as $$m\to\infty$$.

Black and white.

I promise I didn't plan this

#Covid19

Mastodon always 'charges' you 23 characters for every URL you post. It doesn't matter if it is longer or shorter.
There is NO excuse for using URL shorteners which obfuscate your destination if you click - these usually go to fb or twitter, so I Never click them on purpose. They make my browser and I feel dirty.

A special Numberphile on the mathematical modelling of , using the so-called SIR Model. Once again Ben Sparks shows off Geogebra's capabilities.

Also good to see them practising physical distancing!

seed phrase: Marten Kudu Gnat Pony Wasp (HQ: aka-san.halcy.de/quasi/3036078 )

Tech support email: "We encountered many errors while following the instructions published at <address>. Do you have a version without errors?"

Just.... what.

An enjoyable problem (104.B) from the latest Mathematical Gazette: A regular 7-gon is inscribed in the unit circle, with one vertex at (1,0). Find the equations of the two parabolas, symmetric across the x-axis, which pass through the vertices of the heptagon as shown.

@christianp There was that Ivory-soap slogan with 100 in the denominator, but I haven't seen that in years.

Percentages highlight an often-ignored point about rounding: if you've got a boundary, rounding to it can be very misleading.
For example, if something works 999 of 1000 times, it's not correct to say it's 100% effective. 99% is further from the true value, but shows the existence of the failure.

Or, more thrillingly, are there contexts where numbers are written as decimals, but some decimals are illegal?
This is sometimes true for currencies: a price like £1.054 would normally be rounded to the nearest penny. But if it's a price per unit, you might need that extra digit

I've seen gas stations in the US show the tenths part with a fraction instead of a decimal.
Have you seen any other signage with a fixed denominator that isn't 10?

Which numbers can you represent with different notations? For example, decimals represent numbers of the form a×10ᵇ, so not even all of ℚ!
What fruity sets can we find a corresponding notation for?

I want as many different conventions for writing numbers as you can give me. I'm interested in contexts where there are different rules for how numbers are written, e.g. scientific notation, percentages, currencies.
I'm also interested in 'optional' things like grouping digits.

GCompris entertains and educates kids stuck at home. It is available for free for all platforms. Get it here: gcompris.net/index-en.html