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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 12/07/2026

Long time ago I've made a web-version of slides about sliding ladder & Copernicus' thm. Now I'm uploading an English translation: dev.mccme.ru/~merzon/mirror/mp-cat/… (Math is from the book 'Lines and curves', pics were made by M.P.)

A kitten sitting on a ladder leaning against a wall

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 12/01/2026

@dimpase I don't see how an introduction that specifically stresses that «different teams of instructors working with leaflets teach in different ways (…) what follows is a description of how our own particular team worked» makes any claims about the system in general or about any priorities […]

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 12/01/2026

@dimpase > this system wasn't limited to the school #57 of course! but the details are quite different even for different classes in 57 – so the introduction is about how we (one particular team) teach, not about the whole sch. 57 and even less so about «Konstantinov style» teaching in general

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 11/01/2026

a part of the English translation of our book «Basics of Mathematics in Problems (with solutions and comments)» is now freely available at dev.mccme.ru/~merzon/pscache/v08eng… «In the mathematical classes of School #57, the well-know Moscow […] [Original post on mathstodon.xyz]

title page «Basics of Mathematics in Problems»

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 21/12/2025

in quaternions conjugation is a 'polynomial' function: bar q = -1/2 (q + iqi + jqj + kqk) it doesn't contradict anything (and it's easy to prove) but still looks very weird (to me)

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 22/08/2025

…actually this is just a form of CLT and for any polynomial we'll see a normal distribution (maybe after restriction on some arithmetic progression: e.g. if our polynomial is even…) but if we allow polynomials with negative coefficients the situation becomes […] [Original post on mathstodon.xyz]

a curve with a bell-shaped region and some kind of oscilation in the other region

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 22/08/2025

take an arbitrary polynomial P(x) with non-negative coefficients and raise it to a large power we'll get a lot of monomials with various coefficients… let's look not at the individual coefficients but at the plot of all coefficients what will we see? (one can type e.g. something like […]

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 09/07/2025

> It would indeed be super cool to know E8 was the symmetry group of something smaller than the 248-dimensional e8 I've read about E_8 as the symmetry group of octooctonionic (sic) projective plane in some old TWF… […]

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 30/01/2025

@pschwahn sin^(2n)+cos^(2n) is a very simple polynomial of r=cos^2(t): r^n+(1-r)^n now r is almost cos(2t) (more precisely: 2r-1=cos(2t)) but you prefer s=sin(2t)/2… so 4s²+(2r-1)²=1 this should give an explicit formula

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 04/01/2025

an implementation that uses only arithmetical operations (let's see if code formatting works here) ```python from mpmath import mp,mpf,nstr mp.dps = 120 def mysin(x,n): term = x res = x for k in range(1,n): term = -term*x*x / (2*k*(2*k+1)) res += term return res mypi = mpf(3) for k in […]

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 04/01/2025

how to compute (an approximation to) π? one recipe I like: take a couple of iterations of x→x+sin(x) if x=π+ε then x+sin(x)≈π+ε³, so this converges really fast: after just 4 iterations the error is just about 10^{-100} (!) (compare to, say, 1-1/3+1/5-… — where even with 2000 terms the […]

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 10/12/2024

@johncarlosbaez well, there is a natural map to 'my' space {polynomials of the form x³+px+q} from the space of pairs (such polynomial, one of its roots) — and the critical values of this map (aka ramification points) coincide with the discriminant curve so it's essentially the same picture — […]

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 09/12/2024

@johncarlosbaez yes, sure (more precisely 27p²+4q³=0) perhaps the easiest way to find this discriminant curve is to use Vieta: if $t$ is a double root, the other root is $-2t$ (the sum should be 0), so $q=2t^3$, $p=-3t^2$ my favourite fact here is that once this discriminant curve is drawn […]

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 04/12/2024

@highergeometer that's essentially the classical proof by I.Niven (A simple proof that π is irrational, Bull. Amer. Math. Soc. 53 (1947), 509)

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Grigory Merzon @g-merzon.mathstodon.xyz.ap.brid.gy · 27/11/2024

The sum of two cubes, X³+Y³ is divisible by X+Y. What about the sum of three cubes? Well, modulo X+Y+Z we have X³+Y³+Z³=X³+Y³-(X+Y)³=-3X²Y-3XY²=-3XY(X+Y)=-3XYZ. So X+Y+Z divides X³+Y³+Z³-3XYZ. In fact, since X³+Y³+Z³-3XYZ is invariant under (X,Y,Z)→(X,wY,w²Z) with w³=1, we get a complete […]

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