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a part of the English translation of our book «Basics of Mathematics in Problems (with solutions and comments)» is now freely available at https://dev.mccme.ru/~merzon/pscache/v08eng-part.pdf
«In the mathematical classes of School #57, the well-know Moscow secondary school specializing in mathematics, besides lessons in algebra and geometry, there is another subject, traditionally called ‘mathemat
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y=x³+px+q for different (p,q)
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…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 more interesting
pic on the right plots coefficients of (1+3x-x²+x^3)^64…
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Long time ago I've made a web-version of slides about sliding ladder & Copernicus' thm. Now I'm uploading an English translation: https://dev.mccme.ru/~merzon/mirror/mp-cat/index-en.html
(Math is from the book 'Lines and curves', pics were made by M.P.)
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🔥 Top post: a part of the English translation of our book «Basics of Mathema · 34 likes + reposts
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a part of the English translation of our book «Basics of Mathematics in Problems (with solutions and comments)» is now freely available at https://dev.mccme.ru/~merzon/pscache/v08eng-part.pdf
«In the mathematical classes of School #57, the well-know Moscow secondary school speci…
Long time ago I've made a web-version of slides about sliding ladder & Copernicus' thm. Now I'm uploading an English translation: https://dev.mccme.ru/~merzon/mirror/mp-cat/index-en.html
(Math is from the book 'Lines and curves', pics were…
can you believe that conjugation of quaternions is a 'polynomial' function: bar q = -1/2 (q + iqi + jqj + kqk)?
it doesn't contradict anything (in fact, it's easy to prove) but still looks very weird (to me)
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just playing with manim
…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 th…
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 …
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…
how to compute (an approximation to) π?
one recipe (that I recently learned from K.Knop and like a lot): 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 erro…
y=x³+px+q for different (p,q)
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 unde…
https://arxiv.org/abs/2411.07409 (Alain Connes, Joseph Kouneiher)
«This article reflects on the life and mathematical contributions of Pierre Cartier, a distinguished figure in 20th- and 21st-century mathematics. As a key member of the Bou…
https://ojs.ejournals.eu/SHS/article/view/9573/7503
Slava Gerovitch. The Kitchen and the Dacha: Productive Spaces of Soviet Mathematics. Studia Historiae Scientiarum 23 (2024)
«…For many Soviet mathematicians, instead of being a refuge fro…
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