RT @facciobiondate@twitter.com

Sto affettando il primo cocomero della stagione
#Gauss https://twitter.com/facciobiondate/status/1557609376386629632

🐦🔗: https://twitter.com/facciobiondate/status/1672913159160578049

The fascinating Heegner numbers [1] are so named for the amateur mathematician who proved Gauss' conjecture that the numbers {-1, -2, -3, -7, -11, -19, -43, -67,-163} are the only values of -d for which imaginary quadratic fields Q[√-d] are uniquely factorable into factors of the form a + b√-d (for a, b ∈ ℤ) (i.e., the field "splits" [2]). Today it is known that there are only nine Heegner numbers: -1, -2, -3, -7, -11, -19, -43, -67, and -163 [3].

Interestingly, the number 163 turns up in all kinds of surprising places, including the irrational constant e^{π√163} ≈ 262537412640768743.9999999999992500... (≈ 2.6253741264×10^{17}), which is known as the Ramanujan Constant [3].

Some of my notes are here: https://davidmeyer.github.io/qc/galois_theory.pdf. As always, questions/comments/corrections/* greatly appreciated.

#math #galois #gauss #heegnernumber #ramanujan

References
--------------
[1] "Heegner Number", https://mathworld.wolfram.com/HeegnerNumber.html

[2] "Splitting Field", https://mathworld.wolfram.com/SplittingField.html

[3] "Heegner numbers: imaginary quadratic fields with unique factorization (or class number 1).", https://oeis.org/A003173

[4] "Ramanujan Constant", https://mathworld.wolfram.com/RamanujanConstant.html

Born #onthisday, two of everyone's favorites:

https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss and https://en.wikipedia.org/wiki/Claude_Shannon

#gauss #shannon

Qual è la somma dei numeri da 1 a 100?

[parte 2 di 2]

Il giovanissimo Gauss aveva notato che sommando sommando il primo con l'ultimo, il secondo col penultimo, ecc.... otteneva sempre lo stesso risultato:

1+100 = 101
2+99 = 101
3+98 = 101
...

Bastava ripetere l'operazione 50 volte per esaurire i numeri in questione e ottenere che il totale poteva essere calcolato come 50 x 101 = 5050.

Gauss aveva appena scoperto la progressione aritmetica...

#scuola #matematica #gauss

#Gauss
#grouse

Happy birthday to French mathematician, physicist and philosopher Marie-Sophie Germain (1776 – 1831), known as Sophie. She taught herself mathematics using books in her father's library and by corresponding with leading mathematicians of her day, including Lagrange, Legendre and Gauss, …

#linocut #printmaking #sciart #mathart #SophieGermain #ChladniFigures #mathematician #Fermat #womenInSTEM #physicist #elasticity #Gauss #histstm #printmaker #ReliefPrint #WomensHistoryMonth

Le 30 mars 1796, le mathématicien allemand Carl Friedrich #Gauss découvre la construction de l'heptadécagone. #histoire #cejourla #invention

Heute den Gipfel erstürmt, der früher einmal auf dem 10-DM-Schein zu finden war...
Oben pfiff der Wind, die Sonne versteckte sich. Dadurch war der Blick auf die #Hamburg|er Spitzen nicht frei.
#WilsederBerg #Heide #Gauss #Vermessung

Heute den Gipfel erstürmt, der früher einmal auf dem 10-DM-Schein stand...
Ohennpfiff dernWind, die Sonne verstecktensich.
#WilsederBerg #Heide #Gauss #Vermessung

who is #Gauss?

"Riemann’s Seminal Lecture on Non-Euclidean Geometry" by Areeba Merriam 👉 🔗 https://www.cantorsparadise.com/reimanns-seminal-lecture-on-non-euclidean-geometry-11673a8d6fbb

#Riemann #SeminalLecture #NonEuclideanGeometry #EuclideanGeometry #Gravity #DifferentialGeometry #Relativity #GeneralRelativity #SpecialRelativity #RiemannianGeometry #Tensor #Minkowski #HermannMinkowski #Spacetime #Space #Time #Curvature #Klein #Jacobi #Dirichlet #Gauss #Hypersurface #EllipticGeometry #Geometry #Physics #Topology #Hyperspace #Einstein #AlbertEinstein #Isaacson #MichioKaku #Kaku

Always a fun evening whenever Physics Explained uploads a new video (and re-uploads once or twice for minor corrections... I think we got the final version now). This time it's about Heisenberg's uncertainty principle and we randomly perform a Fourier transformation, solve the time-independent wave function, and use Taylor to get the full solution. https://youtu.be/FRP4AqZR3UU

#physics #physik #fysica #natuurkunde #heisenberg #euler #gauss #probability #wavefunction #hbarovertwo #waveparticleduality

Don't know who the Chad was that gave the name to the meme, but the real boss here is Gauss. The math flexes that guy did! That's why I am going to start telling people who accomplish any sort of awesome feat a Gauss or a higa Gauss, depending how amazing the deed.
#math #gauss #chad

https://www.cantorsparadise.com/gauss-bolyai-lobachevsky-the-dawn-of-non-euclidean-geometry-38491218bc89 #Gauss #Bolyai #Lobachevsky #NonEuclideanGeometry

https://www.cantorsparadise.com/gauss-bolyai-lobachevsky-the-dawn-of-non-euclidean-geometry-38491218bc89 #Gauss #NonEuclideanGeometry

#ETechniker gähnen, #Physiker lächeln, Mathematiker sind aus dem Häuschen - nicht grundlos!

Jeder #Mathematiker würde ohne zu zögern sagen: Eine #Gleichung zweiten Grades hat immer zwei Lösungen - nur sind die #Lösungen manchmal „#komplex“ oder "#imaginär". Was genau bedeutet das? Ein Ausflug zur komplexen #Zahlenebene

#Gauss #Quarternionen #Tensoren #Zahlen #FraktaleGeometrie
#Elektrodynamik #Koorddinatensysteme
#Feldtheorie #ReneDescartes #Cartesius #Wurzeln #Euler

https://www.youtube.com/watch?v=sF5kIWCq3D8

Peculiar part of my walk and brain today.

(Context, yesterday I mentioned Gauss' surface integral in passing. I know right, who could resist my conversational charms?)

Today I tried to recall if anything changes for #Gauss' Law in #GeneralRelativity, and I couldn't remember it at all. Not a hint of recollection. My brain stopped at:
Gauss is part of Maxwell and #Maxwell is classical.

Then the walk was beset with worries that something I must've known, surely!? is now gone without trace. In my defence, I've not needed it these last 30 years, but still ... unnerving.

Simple yes / no please. Does the written integral change when applied to / in #GR #spacetime?

TIL: Carl Friedrich Gauss independently invented the Fast Fourier Transform, over 150 years prior to Cooley and Tukey’s 1965 paper introducing the algorithm. Gauss created the FFT to interpolate the orbits of asteroids.

The history of mathematics is littered with near-simultaneous or redundant discoveries; this is the beauty of the decentralized nature of math. No single individual “controls” any area of research, which helps researchers keep each other in check.

#gauss
#math
#research

Composer*
Measuring the World (Film)
Vermessung der WELT
Florian Fitz
*20 November 1974 spielt #GAUSS

*Enis Rotthoff (*1979)
http://de.wikipedia.org/wiki/Enis_Rotthoff
Rotthoff lebt & arbeitet in Berlin & Los Angeles
Musikausschnitte 2 h FILM
https://youtu.be/GV9VmBcO_28

Once in a while, #veritasium creates a video that is stunningly good. This one on #FFT and #nuclear #disarmament was one.

FFTs are something I wish I'd learned in school, and have never taken the time to really learn. This video was the best overview I've seen yet of #fourier transforms. And it also covers the application of FFTs to nuclear treaties, as well as a connection to #Gauss I'd never heard before.

https://www.youtube.com/watch?v=nmgFG7PUHfo