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Maths, jewel-like maths

+Sean Walker makes lovely animations based on maths. This is a real jewel of an animation.

#Maths #Animation
Halloween Pearls

On such precarious threads our lives depend. Meandering about the ghouls and demons on fate's path.

Developed earlier this year. The model maps a plane of hexagonal packed spheres to a sphere using an inverse Mercator transformation.

Developed in python for Blender:

#halloween #Mercator #blender
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Maths, beautiful maths

You must have see the 2-D version of this. (In fact, this animation starts with the 2 D view).

Basically, when you have dots moving with speeds varying sinusoidally on a line, the set of dots seems to rotate.

Now, what that means is, the dots are moving at the same speed _along a circle which you are seeing edge-on.

Confused? See it in 3D to understand how that works.

Thanks to +Utkrisht Seth for sharing.
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Maths, lovely maths | Animation

This cute thing shows what happens when you rotate each rod in each ring in turn by a fixed amount, ring by ring.

Via +Panah Rad
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Maths, mind-bending maths

That image is the representation of a prime number. It was generated for the school whose logo it resembles, and it also has the same number of digits as the year the college was founded.

A Sign from On High? Nothing quite so esoteric. It's apparently quite easy to generate these....

Read on, and find out all about it in +Kam-Yung Soh's post.

#Maths #PrimeNumber
Fascinating. Probably lots of scope for finding other primes that produce other images. There's one of Corpus Christi College also in the link. "On Thursday, Numberphile published this video, which features a startling wall hanging in the Senior Combination Room at Trinity Hall, Cambridge: Junior research fellow James McKee devised a 1350-digit prime number whose image forms a likeness of the college’s coat of arms. (The number of digits is significant, as it’s the year that Bishop William Bateman founded the college.)

It turns out that finding such “prime” images is easier than one might think. In the video description, McKee explains: “Most of the digits of p were fixed so that: (i) the top two thirds made the desired pattern; (ii) the bottom third ensured that p-1 had a nice large (composite) factor F with the factorisation of F known. Numbers of this shape can easily be checked for primality. A small number of digits (you can see which!) were looped over until p was found that was prime.'”"

+Richard Green +John Baez
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Maths, lovely maths | Rotating cones

+Sean Walker brings us another lovely maths animation, complete with shiny reflections.

#maths #art #mathart #animation
Conic Stalagmites and Stalactites

Ideological thinking leaves no space for self-realization.

A side by side variation of the conic animation model.

Developed with Python in Blender:

#mathart #cones #animation
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Maths, lovely maths | Animation

+Sean Walker has come up with this beautiful animation.

To me, it looks like rotating cones. What does it look like to you?

#MathsLovelyMaths #Maths #Animation #Art #MathsArt
My first animation in quite some time...

Simple but I think interesting. I also employed a new technique in which I 'crease' the edges of the surface segments and perform a smoothing to create more photo-realistic surfaces.

#cones #animation #blender
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Maths, lovely maths

Always, you hear the plaintive cries, But is it useful in real life? when it comes to maths.

Who knows? Stuff that used to be pure maths finds strange and lovely applications, sometimes centuries later.

Enjoy maths!

Practical uses will follow.

<end of motivational speech>

Via +God Emperor Lionel Lauer

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Maths, lovely maths | Hand calculating square roots

We were taught how to do square roots in class 7, I think. I never did understand how it worked, unlike say, long division, so I'd pretty much forgotten it soon after I got a calculator, and had to struggle a bit when I attempted it a few years ago (wikipedia, bless you).

However, this explanation which +Kam-Yung Soh has unearthed is lovely, and I'm more likely to remember the method now.

He's also found this wikipedia page which starts out simple and then goes into esoteric algorithms and methods suitable for computers (which have no hands, so they're not hand calculating, and you can stop reading or skip sections if you only want hand calculations).

On the other hand, I'm more likely to use the Babylonian method, now that I know it exists! :D

Who knew simple things like square roots could be so fascinating, so simple, so complex, and so delightful?

#MathsLovelyMaths #maths #SquareRoots #HandCalculations
Oh, this is wonderful. A post on how to manually calculate square roots. Useless in practice, of course, but who cares! "The calculator knows the answer. I don’t know how, but it does. And well, that’s where the story ended.

Good enough, yeah?

But this is about so much more than solving an already solved problem.

It’s about finding beauty in the mundane. About understanding something not because you have to, but because you can. And it’s about seeing how every ounce of mathematics has been fought for, discovered, and sifted from a greater logical system.

Ready to take a quick trip through the lost art of solving square roots?"

+Richard Green
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Maths | The Inspection Paradox

So just why is it that we almost never get a taxi when we really need one? How come the train is almost always later when we wait for it?

Welcome to the Inspection Paradox.

In a nutshell, you'll see more of the longer/bigger thing than 'the real number', whether it is waiting time, class size, overcrowded planes, or whatever. It really is true that the lane you join moves slower. Now you can know why.

(Dunno if it will make you feel better, though).

This lovely article was found by +Sameer Bora, and posted on fb.

#maths #Statistics #InspectionParadox
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