I was a guest on the first episode of a new maths series, Un-Natural Numbers, with Ben Cornish.
The idea is that in episode N, the guests present their favourite facts about the number N.
For episode 1, I talked about Legendre's constant. The host, Ben Cornish, talked about Benford's Law, and Paddy Moore talked about infinite series that sum to 1.
maths
News about a new, open-access journal covering original work in the intersection of mathematics and fibre/fiber arts.
Details are on the website :
Looks intriguing!
This *definitely* needs to get outside my bubble, so boosts are especially welcome, and if people can suggest more hashtags, that would be great.
#FibreArt #FiberArt #Mathematics #Math #Maths #Journal #Knitting #Crochet #Weaving
More hashtags suggested ... adding here as an edit ... not all are applicable, but ... who knows!
#Knitting #Knitstodon #FiberArts #FibreArts #NeedleArts #Maker #Creator #Crafts #HandMade #SurfFeeds
#PrintMaking #Woodcut #Art #HandMade #Analog #Arte #Xilografia #Grafica #ArtIsForEveryone
Thank you for your indulgence ...
Edited 8d ago
The Fourier Transform is a mathematical operation that transforms a function of time (or space) into a function of frequency. It decomposes a complex signal into its constituent sinusoidal components, each with a specific frequency, amplitude, and phase. This is particularly useful in many fields, such as signal processing, physics, and engineering, because it allows for analysing the frequency characteristics of signals. The Fourier Transform provides a bridge between the time and frequency domains, enabling the analysis and manipulation of signals in more intuitive and computationally efficient ways. The result of applying a Fourier Transform is often represented as a spectrum, showing how much of each frequency is present in the original signal.
\[\Large\boxed{\boxed{\widehat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,\mathrm dx, \quad \forall\xi \in \mathbb{R}.}}\]
Inverse Fourier Transform:
\[\Large\boxed{\boxed{ f(x) = \int_{-\infty}^{\infty} \widehat f(\xi)\ e^{i 2 \pi \xi x}\,\mathrm d\xi,\quad \forall x \in \mathbb R.}}\]
The equation allows us to listen to mp3s today. Digital Music Couldn’t Exist Without the Fourier Transform: http://bit.ly/22kbNfi
#Fourier #FourierTransform #Transform #Time #Frequency #Space #TimeDomain #FrequencyDomain #Wavenumber #WavenumberDomain #Function #Math #Maths #JosephFourier #Signal #Signals #FT #IFT #DFT #FFT #Physics #SignalProcessing #Engineering #Analysis #Computing #Computation #Operation #ComplexSignal #Sinusoidal #Amplitude #Phase #Spectra #Spectrum #Pustam #Raut #PustamRaut #EGR #Mathstodon #Mastodon #GeoFlow #SpectralMethod
Edited 70d ago
#mathematics question: is there any good collection of all the knowledge about Conway's "nimbers"? I've found any number of beginners' explanations, but nothing further.
(I mean the thing that makes a field of characteristic 2 out of ℕ₀, with addition corresponding to bitwise XOR, and multiplication a really weird inductively defined thing, such that every initial segment of ℕ₀ of size 2^{2^n} forms a subfield.)
I was idly playing around with them recently – wrote a tiny Python thing to implement their multiplication. I happened across the fact that in each of the first nine of those finite subfields, the _largest_ integer in that subfield – 2^{2^n}-1 – generates its whole multiplicative group. That is, 3 has order 3, 15 has order 15, 255 has order 255, … up to and including 2^512−1.
Is that true for all n? I'm curious to know if this is a known result, or at least a known conjecture. Seems to me it would be pretty neat if it were true, because it would give you a "canonical" choice of primitive polynomial over GF(2) of degree 2^n – just take the min poly of the corresponding nimber.
By my calculations, the first few of those polynomials (in the usual binary representation where 2^n stands in for x^n) are 3, 7, 25, 425, 101021, 7158330089, 27971386341277386797. But OEIS doesn't know that sequence, so maybe this isn't known?
Teach #Maths or #Programming? Looking for a creative project that links to D&T? Join my free online #TurtleStitch training session on 5th March 16:00 GMT to explore #CreativeComputing & #Embroidery.
Sign up: www.warwick.ac.uk/turtlestitch
I'm looking for some pointers...
I have a vector in 3D space. I want to be able to manipulate its direction based on input pan and tilt angles... Importantly I'd like to be able to give these angles as absolute (i.e: from "up") or relative (i.e: from the current direction).
I have a working solution, but I suspect there's a more efficient way to do this. I had a stab with Quaternions, but I couldn't get the tilt to behave like it would on a gimble.
Any ideas? 🧮
" 𝗠𝗮𝘁𝗵𝘀 𝗣𝗿𝗼𝗼𝗳𝘀 𝗶𝗻 𝗟𝗲𝗮𝗻 - 𝗙𝗶𝗿𝘀𝘁 𝗦𝘁𝗲𝗽𝘀 " 🚀
Designed specifically for beginners struggling to get started with other courses and guides.
* Simple bite-sized examples.
* Focus on concepts, introduced gradually.
* One easy exercise per chapter.
.. all to build confidence, not demolish it !
Edited 111d ago
Take the parity of the indices of the terms of the continued fraction of Liouville's constant that equal 8. For odd numbers turn left, for even turn right.
What do you get?
The Dragon curve appears, again. It's everywhere.
This works with indices equalling 1 too (for 9 you'll have to ignore the first digit)
I am a #maths educator #teaching near #Paris, in #France.
Science-wise, I am interested in maths and #computer #science, particularly in some fields at the intersection of these two: algorithmic number theory, computer #algebra, #cryptography, coding theory... And I love to teach!
I also like #politics, #games of all types, #improv (theatre), #reading. I toot in French when I think that mostly French people could be interested.
And I might talk about #parenting since I'm a dad!
I forgot to do an #introduction, so hi!
Professionally I make #computers go "beep" and occasionally "boop" if I'm feeling fancy. On the Bad Place I mostly post elaborate #puns and describe ways my kids (aka #hatchlings) have outsmarted me. Used to run a #BoardGames group but rarely find the time now, sadly. Interested in #maths, #science, #language, #puzzles, #VideoGames and probably #OtherThingsThatIHaveForgotten.
Not sure exactly how I'll use #Mastodon - work in progress...
(0/13)A 🧵 about helping children you care about to learn maths. And you don't even have to be a mathematician, or even "good" at #maths, to do it. You just have to model resilience and positivity towards what they're doing, and to avoid reinforcing negative tropes.Here's how:
If you are interested in #decolonizing and #diversifying academia, we recently started a podcast on the topic. In this month's episode I had the privilege of speaking with @chadtopaz about #equity on #STEM subjects. Currently on spotify, apple, stitcher, pocketcasts! #maths
#Mathematics / #Maths / #Math picks of the day:
➡️ @EuroMathSoc - European Mathematical Society
➡️ @SydMathInst - Sydney Mathematical Research Institute
➡️ @hermathsstory - Highlighting women in world of mathematics
➡️ @mathsgear - Shop making & selling fun nerdy maths dice, puzzles, games, books etc
➡️ @MathsJam - Monthly real life events for maths enthusiasts
➡️ @carnivalofmaths - Monthly roundups of interesting maths
➡️ @TMiP - Conference for mathematics communicators
🧵 1/7
#tinyCSStip Want to create a triangle with all edges equal in 4 simple #CSS declarations?
Such a triangle also has all vertex angles equal = (sum of angles in a triangle)/3 = 180°/3 = 60°
👉 https://en.wikipedia.org/wiki/Sum_of_angles_of_a_triangle
Knowing its edge length a, its height is a·sin(60°).
Aspect ratio of the box
a/(a·sin(60°)) = 1/sin(60°)
#cssMaths #Maths #Mahematics #code #trigonometry #triangle #coding #webDev #frontend #web #webDevelopment #dev
Hello everyone! Here's my #introduction...
I'm a software engineering manager at #microsoft, living in the #uk. I'm interested in #science, #technology, and #oss #development.
I tend to favour #python when #programming, and spend most of my time in #vscode.
In my spare time I like #running, #cycling, #beer, and am enjoying studying for a #maths degree with the #openuniversity.
Please recommend #books about #maths that *aren't* about teaching it.
I'm looking for books that someone might sit and read for pleasure rather than for academic reasons (so not really textbooks, but I guess there might be some really compelling textbooks out there). Fact or fiction. Feel free to define "about maths" however you like (there may be points for really inventive interpretations). They might only be loosely about maths, but I'll set the criterion that someone who thinks they're not into maths would recognise it as maths.
Go!
New #OffGridPod, in which we make noises about #maths games, and hear the best #Olympics fact ever. #podcast #quiz https://offgrid.tlmb.net/2024/08/25/biggles-fractal-trap-ep-43/
Concentration of measures:
Talagrand's "work illustrates the idea that the interplay of many random events can, counter-intuitively, lead to outcomes that are more predictable, and gives estimates for the extent to which the uncertainty is reigned in."
Marianne Freiberger: https://plus.maths.org/content/abel-prize-2024 @data @mathematics
#maths #mathematics #Talagrand #data #probability #magnets #spinGlasses #physics
An #introduction is in order.
I'm a stay-at-home dad living in Boorloo (Perth) with experience in: #programming, #maths, #prisons, #aod, #addiction, and #volunteering.
Things I like to read about:
#JuliaLang :julialang:
#Maths
#AusPol (but only policies and elections, not game-playing rubbish)
#Indigenous experiences
#TransRights
#DisabilityJustice
#Feminism
#Masculinity
#FuckPatriarchy
#FuckWhiteSupremecy
Things I like to post about:
#cats (we have a #RescueCat called Sancho)
#SocialJustice
#ActuallyAutistic
#Volunteering
Things I like, but don't read or post about:
#jazz and #swing
#mcu
#MurderMysteries from #AgathaChristie through #MidsommerMurders to #KnivesOut
#CrypticCrosswords
#Cubing
#ttrpg
#videogames
Noise Bullseye
Experimenting with semi-random noise in Processing. In this generative art piece I programmed it so that each pixel has a random lightness and the lightness is biased towards a certain value. That value is determined by the sine function, which is plotted in polar coordinates.
You'll notice that there are rings of pure black... This is due to the value of the sine function being zero (I used sin( r/20 ) + 1 so the the area where the sine is zero is stretched out) and the fact that the lightness of each pixel is obtained by multiplying by the sine function. So the lightness of these pixels is a random value multiplied by the sine at that location, which ends up being zero.
I like how the result ended up looking like a 3D styrofoam bullseye.
#Art #ArtistOfMastodon #Abstract #AbstractArt #Generative #GenerativeArt #Math #MathArt #Maths #Mathematics #MathematicalArt #Geometry #Geometric #GeometricArt #Coding #Programming #Algorithm #Processing
Today's #BigMathOff match hasn't had many votes, which is a shame because they're two lovely mathematical thoughts.
If you've got a moment, go and have a look, and let us know which one you liked best: https://aperiodical.com/2024/07/the-big-internet-math-off-2024-quarter-final-3/
Hello #maths fans (and #math fans too!). I'm taking part in some competitive writing themed on mathematics. You have from now until 0800BST (0700UTC) on Saturday to vote. See https://aperiodical.com/2024/07/the-big-internet-math-off-2024-round-1-match-5/
Hello #maths fans! There is a competition starting today involving 16 mathematicians showcasing topics they think are interesting. Round 1 Match 1 is open until 0800BST (0700 UTC) tomorrow morning - take a look at https://aperiodical.com/2024/07/the-big-internet-math-off-2024-round-1-match-1/ and vote for your favourite!
I'm taking part in this but you'll need to wait until Friday to see my entry. But do check back in the days between now and then to see what others have to offer.
Good luck to the #BigMathOff competitors!
Edited 335d ago
I've done it! After literal months of work, I've finally finished my (rather long) blog post about how AES-GCM works and how it's security guarantees can be completely broken when a nonce is reused:
It includes more than 10 interactive widgets for you to try out AES-GCM, GHASH and the nonce reuse attack right in your browser! (Powered by #RustLang and #WASM )
If you're interested in #cryptography , #math (or #maths ) or #infosec you might find it interesting.
If you do read it, I'm all ears for feedback and criticism!
#Introduction I am a #humanist #skeptic #atheist. I love #maths, #science, #history, and #nature, especially cats and birds of prey. I work in tech/customer support. I speak a little Spanish and dabble in several languages. I'm a fan of Terry Pratchett. I'm a gamer. I am probably neurodivergent. I follow far too many podcasts.