beandev, to mathematics
@beandev@social.tchncs.de avatar

>> Prime Number Puzzle Has Stumped Mathematicians for More Than a Century

"Experts have only started to crack the tricky twin prime conjecture"

https://www.scientificamerican.com/article/prime-number-puzzle-has-stumped-mathematicians-for-more-than-a-century/

gutenberg_org, to books
@gutenberg_org@mastodon.social avatar

British mathematician Charlotte Scott was born #OTD in 1858.

Her research focused on algebraic geometry, a field dealing with solutions to systems of polynomial equations. Notable works include her paper on binary forms and her research on the properties of algebraic curves. She co-authored "An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry," which became a widely used textbook. She was awarded an honorary degree by the UPenn in 1906.

#books #mathematics

gutenberg_org, to mathematics
@gutenberg_org@mastodon.social avatar

Irish mathematician Alicia Boole Stott was born in 1860.

She discovered & described many four-dimensional polytopes & coined the term “polytope” to generalize polygons & polyhedra to higher dimensions. She extensively used Schläfli symbols to categorize and describe polytopes. Later in life, Alicia worked with Harold Coxeter and their collaboration furthered the understanding of regular polytopes and three-dimensional projections of four-dimensional figures.

metin, to math
@metin@graphics.social avatar
Le_bottin_des_jeux_linux, to linuxgaming
@Le_bottin_des_jeux_linux@floss.social avatar

💡 Did you know it?
🕹️ Title: Immersive linear algebra
🦊️ What's: (online) mathematics with interactive illustration
🏡️ https://immersivemath.com/ila/index.html
🔖 #LinuxGaming #ShareYourGames #ELearning #Mathematics
🦣️ From: https://mastodon.cloud/@boilingsteam/112427672135539688
🦉️ https://www.youtube.com/embed/TIcSnsmitHw

blaue_Fledermaus, to math
@blaue_Fledermaus@mstdn.io avatar

people, if two parallel lines meet at infinity, can it mean they form a polygon?

gutenberg_org, to books
@gutenberg_org@mastodon.social avatar

French mathematician Évariste Galois died #OTD in 1832.

Galois developed a deep understanding of the relationship between polynomial equations and group theory. He showed how the solutions to polynomial equations are related to the structure of certain groups, now called Galois groups. This connection helps determine whether a polynomial can be solved by radicals (i.e., using a finite number of root extractions).

Galois at PG:
https://www.gutenberg.org/ebooks/author/40484

#books #mathematics

This is the beginning part of paper to apply for a contest. Évariste Galois — Dupuy, Paul

gutenberg_org,
@gutenberg_org@mastodon.social avatar

«Je rêve d'un jour où l'égoïsme ne régnera plus dans les sciences, où on s'associera pour étudier, au lieu d'envoyer aux académiciens des plis cachetés, on s'empressera de publier ses moindres observations pour peu qu'elles soient nouvelles, et on ajoutera " je ne sais pas le reste".».

~Évariste Galois (25 October 1811 – 31 May 1832)

#books #mathematics

mkwadee, to mathematics
@mkwadee@mastodon.org.uk avatar

Forgive the recent apparent obsession (I’d call it a fascination) with the but I’ve just discovered something I’d not heard of before. It is also called a or curve, which means that a particle starting from any location on the curve will get to the at precisely the same time as a particle starting at any other point.

An animation showing a particles starting at various points on a cycloid but all reaching the minimum point simultaneously.

Le_bottin_des_jeux_linux, to linuxgaming
@Le_bottin_des_jeux_linux@floss.social avatar
OscarCunningham, to math
@OscarCunningham@mathstodon.xyz avatar

For a long time I felt like I didn't really understand the Yoneda Lemma. I knew some things that people said about it ('we can understand objects by the maps into them' and 'the Yoneda embedding is full and faithful') but the statement 'Hom(Hom(A, -), F) = F(A)' itself was something I could only use as a symbolic manipulation without understanding.

On the other hand, I did separately know facts like 'In the category of quivers there are objects which look like • and •→•, such that the maps out of them tell you exactly the vertices and edges in your quiver' and 'In the category of simplicial sets there are objects which are just an n-simplex; maps out of them are the n-simplices of the object you are mapping into'.

Somehow I only recently realised that these examples are precisely the Yoneda Lemma. These objects are precisely presheaves of the form Hom(A, -), and the Yoneda Lemma tells you what you get when you map out of them.

In particular I think it would be useful to give the quiver example to students when they learn the Yoneda Lemma.

gutenberg_org, to mathematics
@gutenberg_org@mastodon.social avatar

Serbian mathematician, astronomer, climatologist Milutin Milanković was born #OTD in 1879.

He is best known for his theory of climate change (Milankovitch cycles), which explains the long-term cycles in Earth's climate based on changes in its orbit and orientation relative to the Sun. He used his expertise in mathematics to develop detailed models of how these orbital changes influence the distribution of solar radiation on Earth’s surface.

https://web.archive.org/web/20120419011102/http://www.climatedata.info/Forcing/Forcing/milankovitchcycles.html

#climatology #mathematics

Adorable_Sergal, to random
@Adorable_Sergal@hachyderm.io avatar

I feel like I would've been more into mathematics if it involved a lot of candles and wearing cultist robes

Adorable_Sergal,
@Adorable_Sergal@hachyderm.io avatar

I genuinely think that a fanatical emphasis on real world uses has done more to harm mathematical literacy than any other academic policy.

Kids love weird shit, and teachers should 100% take advantage of that and roll into class bein' like "Ok nerds, here's the math that proves you're a donut"

#math #mathematics

dmm, to math
@dmm@mathstodon.xyz avatar

Here I tried to prove the Existence Theorem for Laplace Transforms. I don't know what the/a "conventional proof" looks like, but this is what I came up with.

A few of my notes on this and related topics are here: https://davidmeyer.github.io/qc/dirac_delta.pdf

As always, questions/comments/corrections/* greatly appreciated.

#laplacetransform #existencetheorem #math #maths #mathematics

gutenberg_org, to books
@gutenberg_org@mastodon.social avatar

French mathematician Abraham de Moivre was born #OTD in 1667.

He is best known for de Moivre's theorem, which links complex numbers and trigonometry, and for his work in the development of analytic geometry and the theory of equations. He published "The Doctrine of Chances" (1718) where he developed a formula for the normal approximation to the binomial distribution, now known as the de Moivre-Laplace theorem.

https://en.wikipedia.org/wiki/De_Moivre%27s_formula

https://en.wikipedia.org/wiki/De_Moivre%E2%80%93Laplace_theorem

#books #science #mathematics

The doctrine of chances: or, a method of calculating the probabilities of events in play, by A. de Moivre .... - London : printed for A. Millar, in the Strand, 1761. - [4], xi, [1], 348 p. ; 4º .

mkwadee, to animation
@mkwadee@mastodon.org.uk avatar

A couple of weeks ago, I posted an #animation of a point on a circle generating a #cycloid.

If you turn the curve "upside down", you get the #BrachistochroneCurve. This curve provides the shortest travel time starting from one cusp to any other point on the curve for a ball rolling under uniform #gravity. It is always faster than the straight-line travel time.

#MyWork #CCBYSA #Mathematics #Maths #AppliedMathematics #Physics #Calculus

Balls rolling under gravity on a cycloid and on straight lines inclined at various angles.

mkwadee,
@mkwadee@mastodon.org.uk avatar

This is an interesting problem in #ClassicalMechanics and exercised luminaries like #Newton and #Euler. I think the latter's use of the #CalculusOfVariations is a stroke of genius.

#MyWork #CCBYSA #Mathematics #Maths #AppliedMathematics #Physics #Calculus

mkwadee,
@mkwadee@mastodon.org.uk avatar

Anyway, the #animation took a bit of thought as it requires a bit of #Mechanics, some #Integration and is made a bit more tricky as the curve is multi-valued and so you need to treat different branches separately. The #AnimatedGif was produce with #WxMaxima.

#MyWork #CCBYSA #Mathematics #Maths #AppliedMathematics #Physics #Calculus

dmm, to math
@dmm@mathstodon.xyz avatar

Here's something I just learned: the lucky numbers of Euler.

Euler's "lucky" numbers are positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k² − k + n produces a prime number.

Leonhard Euler published the polynomial k² − k + 41 which produces prime numbers for all integer values of k from 1 to 40.

Only 6 lucky numbers of Euler exist, namely 2, 3, 5, 11, 17 and 41 (sequence A014556 in the OEIS).

The Heegner numbers 7, 11, 19, 43, 67, 163, yield prime generating functions of Euler's form for 2, 3, 5, 11, 17, 41; these latter numbers are called lucky numbers of Euler by F. Le Lionnais.

h/t John Carlos Baez
(@johncarlosbaez) for pointing this out.

References

[1] "Lucky numbers of Euler", https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler

[2] "Heegner number", https://en.wikipedia.org/wiki/Heegner_number

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

[4] "Euler's "Lucky" numbers: n such that m^2-m+n is prime for m=0..n-1", https://oeis.org/A003173

#luckynumbersofeuler #heegnernumber #euler #math #maths #mathematics

dmm, to math
@dmm@mathstodon.xyz avatar

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} ≈ 262537412640768743.99999999999925... (≈ 2.6253741264×10^{17}), which is known as the Ramanujan Constant [4].

A few of my notes on this and related topics are here: https://davidmeyer.github.io/qc/galois_theory.pdf. As always, questions/comments/corrections/* greatly appreciated.

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

#galois #gauss #heegnernumber #ramanujan #math #maths #mathematics

fractalkitty, (edited ) to math
@fractalkitty@mathstodon.xyz avatar

I am super excited for my friend Paulina's new book:

Mapmatics: A Mathematician's Guide to Navigating the World

If anyone in the media space is interested in doing a book review, please DM me, and I can provide information on how to get an advanced copy.

https://www.amazon.com/gp/product/0674294238

MathOutLoud, to math
@MathOutLoud@mathstodon.xyz avatar

A nice viewer submitted problem today dealing with the range of values of a function. See my thought process and solution here:

https://youtu.be/KcCvTZDWbAU

#math #maths #mathematics

LabPlot, to datascience
@LabPlot@floss.social avatar

Below is just a small sample of plots that were created with #lLabPlot.

@labplot

#LabPlot is a FREE, open source and cross-platform Data Visualization and Data Analysis software.

Would you like to share with us your plots made in LabPlot?

#DataAnalysis #DataScience #Data #DataViz #DataVisualization #Science #Statistics #Mathematics #Math #STEM #FOSS #FLOSS #OpenSource #KDE

quantarss, to mathematics
@quantarss@newsmast.social avatar
LabPlot, to datascience
@LabPlot@floss.social avatar

Do you know Paul F. Velleman's Fourteen Data Aphorisms for Data Analysis ❓

@labplot

➡️ https://en.wikipedia.org/wiki/Paul_F._Velleman

1/ Let's read carefully and think about the first of the aphorisms.

What does it mean to you ❓

#Aphorism #DataAnalysis #DataScience #Data #DataViz #Science #Statistics #LabPlot #FOSS #FLOSS #OpenSource

LabPlot,
@LabPlot@floss.social avatar
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