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#maths

1 post1 participant1 post today
Public
Fractal Kitty

I have posted the 238th Carnival of Mathematics!

fractalkitty.com/238th-carniva

If I missed something please let me know.

There is an extremely slow bit of javascript for untouchable numbers that hopefully won't make the post untouchable.

Thank you @aperiodical for organizing this.

This month we have posts from @mjd Peter Cameron, @two_star, @j2kun, Brian Clegg, @fortnow @KarenCampe, Amédée d'Aboville, Ed Vogel, @standupmaths

There was also an amazing amount of math and art being shared on blueSky with @Ayliean 's math art March prompts

what appears to be a grey circle made of circles, but is created from a K238 graph where there are 238 dots around a circle that connect to every other dot.
#carnivalOfMathematics#indieweb#blogCarnival
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Pustam | पुस्तम | পুস্তম🇳🇵

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: bit.ly/22kbNfi

Gizmodo · Digital Music Couldn't Exist Without the Fourier TransformThis is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny
#Fourier#FourierTransform#Transform
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Pustam | पुस्तम | পুস্তম🇳🇵

An aerospace engineering student from the Pennsylvania State University refines a 100-year-old math/aerodynamic (wind energy equation) problem, expanding wind energy possibilities.

Article published in Wind Energy Science:
wes.copernicus.org/articles/10

Read more:
[1] timesofindia.indiatimes.com/ed
[2] psu.edu/news/engineering/story

wes.copernicus.orgGlauert's optimum rotor disk revisited – a calculus of variations solution and exact integrals for thrust and bending moment coefficientsAbstract. The present work is an amendment to Glauert's optimum rotor disk solution for the maximum power coefficient, CPmax, as a function of tip speed ratio, λ. First, an alternate mathematical approach is pursued towards the optimization problem by means of calculus of variations. Secondly, analytical solutions for thrust and bending moment coefficients, CT and CBe, are derived, where an interesting characteristic is revealed pertaining to their asymptotic behavior for λ→∞. In addition, the limit case of the non-rotating actuator disk for λ→0 is shown for all three performance coefficients by repeated use of L'Hôpital's theorem, and its validity is discussed in the context of other works since Glauert.
#Aerospace#Science#Math
Public
Wen

Continuity/Fact checking of the moment - Prime Target

Apple have been showing ‘Prime Target’ - an occasionally amusing, almost always silly thriller based around the premise that codes based on prime numbers can be easily cracked (short form explanation). But when our heroes make of in a #Swastikar (Tesla) the dubbed sound is of a combustion engine 🙄. Who got that wrong?

Well it amused, even if the history and maths were suspect

#PrimeTarget#Silly#AppleTV
Public
ƧƿѦςɛ♏ѦਹѤʞ

“I created an addendum to Glauert’s problem which determines the optimal aerodynamic performance of a wind turbine by solving for the ideal flow conditions for a turbine in order to maximize its power output”.
#maths #aerospace #WindPower #WindEnergy #WindTurbine #aerodynamics #DivyaTyagi #mathematics #physics #technology
psu.edu/news/engineering/story

Public
Christian Lawson-Perfect

Last Summer, my student intern Scarlett Spackman put together a great document about accessible teaching for #maths, #stats and #physics.
Under two headers, "Why should I care?" and "Advice", Scarlett makes the case for improving accessibility and then offers practical ways of achieving that.

I've finally got the go-ahead to share it more widely:

mas.ncl.ac.uk/accessible-teach

www.mas.ncl.ac.ukAccessible teaching for Maths, Stats and Physics
#accessibility#teaching#MathEducation
Public
Her Maths Story

Hello, world! We’re back from our break & ready to start afresh. This incorporates decisions we made + changes we’re implementing to keep going forward in a way aligning with our values & underlining our ambition to celebrate diversity in #maths + highlight women in the field.

We’re excited to announce that we’re now on Bluesky! 🦋🎉 You can find us under our usual handle @hermathsstory.bsky.social.

We’re looking forward to many interactions with you - and stay tuned because we have new amazing stories coming up!

Today’s quote is not from a featured story but from Shakuntala Devi. She was an Indian writer and mental calculator, popularly known as the “human computer”.
Photo credit: Public domain

Black-and-white image of Shakuntala Devi in the background, wearing a flower necklace and smiling. On the top right the quote "Immorality does not consist in being different. It consists in not allowing others to be so." Shakuntala Devi
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Dani Laura (they/she/he)

After my previous wrong attempt, here another aperiodic tiling decompositions I found. The base tile is made by joining three equilateral hexagons (I call it a trihex), colored with two different colors depending on orientation. Two possible decompositions, one has central symmetry, the other is asymmetric (in fact there are more, these are the simplest ones). The decompositions produce tiles rotated arctan(√3/15) ≅ 6.587⁰
#TilingTuesday #tiling #Maths

Replied in thread
Public
💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

@andypiper
"You can’t be on the social web without being social"
That's basically what I say to those who say they're not getting any #engagement on #Mastodon... but also everything they #post is all #business! Don't just be a #programmer, or a #founder, be a PERSON. I have some #followers from posting about #tech, and I have some followers from posting about #Maths, but also some who just liked what I #boost or what I said when I replied to someone about something else altogether, like now! 🙂

Public
groff

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)

Dragon Curve rendered in red, yellow and white on a black background, the colours are based on the number of times a turn is reversed during it's construction.
#maths#math#mathematics
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