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Tamás Görbe Profile picture
@TamasGorbe
Mar 28, 2019 • 3 tweets • 2 min read • Read on X
The composition of two harmonic motions with frequencies ω and ω' produces the beautiful Lissajous curves: x=cos(ωt), y=sin(ω't). [Wiki bit.ly/2HJB4v8] Inspired by @juliomulero. #50FamousCurves
How to draw Lissajous curves? Build a pendulum whose length is different in perpendicular directions. The pendulum will trace a Lissajous curve. [Source: ]
Lissajous curves on an oscilloscope #50FamousCurves

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More from @TamasGorbe

Tamás Görbe Profile picture
Oct 19, 2022
Gabriel's Horn is a solid you get by rotating the hyperbola y=1/x (with x>1) about the x-axis.

Having finite volume (π) and infinite(!) surface area, it leads to the apparent paradox:

"You can fill it with paint, but you cannot coat it." Image
The moral of this example is that infinity is a tricky concept and we need to be very careful with trusting our intuition when it comes to ∞.
The number of times I've seen people write things like

“∞ – ∞ = 0” or “∞ ÷ ∞ = 1”
Read 4 tweets
Tamás Görbe Profile picture
May 31, 2021
NEW PAPER
Free to read rdcu.be/clsVe

Earlier this year a friend* and I've solved a long-standing problem which, in part, meant finding the eigenvectors of this matrix. In this thread, I'll review our result and bits of 170 years of history

*J.F. van Diejen, Talca

1/n Image
The title of our paper is "Elliptic Kac–Sylvester Matrix from Difference Lamé Equation" and it was recently published in the mathematical physics journal Annales Henri Poincaré.

Article page: doi.org/10.1007/s00023…

2/n Image
Just to "name-drop" some of the characters that will appear in the story: Sylvester (duh), Jacobi, Boltzmann, two Ehrenfests, Schrödinger and Kac (obvs).

(I'll expand the thread over several days so please be patient.)

3/n
Read 33 tweets
Tamás Görbe Profile picture
Nov 17, 2020
"Here's a photo of my boy, Peter. He doesn't yet know what the continuum is, but he doesn't know what fascism is either." - George Szekeres' message to Paul Erdős.
Peter Szekeres was born in Shanghai, where his parents George Szekeres and Esther Klein escaped from Nazi persecution in 1938.
Happy Ending Theorem: any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.

Erdős gave this name to the theorem, because it led to the marriage of Szekeres and Klein
Read 4 tweets
Tamás Görbe Profile picture
Oct 13, 2020
As a run-up to the "Introduction to Integrability" series (see my pinned tweet), I decided to share some interesting bits from the history of integrable systems.

Let's start at the beginning, shall we? So Newton... Image
#1 It all started with Newton solving the gravitational 2-body problem and deriving Kepler's laws of planetary motion as a result. I would argue that this was possible, because the Kepler problem is (super)integrable. [1/2] Image
This roughly means that there are many conversed physical quantities like energy, angular momentum, and the Laplace-Runge-Lenz vector. These conservation laws restrict the motion and allow for explicit analytic solutions of otherwise difficult equations. [2/2] Image
Read 5 tweets
Tamás Görbe Profile picture
Oct 12, 2020
I'm happy to announce "Introduction to Integrability", a series of 5 online lectures covering the basics of my research area, Integrable Systems.

The first lecture is on Thursday 22 October 3:30pm (BST).

You can register here:
icms.org.uk/V_INTERGRABILI…
The series is funded by the London Mathematical Society. It's also supported by ICMS as part of the ICMS Online Mathematical Sciences Seminars.
The series is targeted at postgraduate students, but everyone interested in learning about integrable systems is welcome.

A basic understanding of classical and quantum mechanics will be assumed.
Read 11 tweets
Tamás Görbe Profile picture
Sep 2, 2020
I thought of an integer between 1 and 100.

How many yes-no questions do you need me to answer so you find this number if you don't want to rely on luck?
What if you have to send me the full list of your questions first? How many questions will you need then?
How long is your list of yes-no questions if you know that I will forget to answer one of the questions?

(You will see which question is unanswered in my reply.)
Read 5 tweets

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