# mathematical shapes

Tatuaje de una espiral dorada que incluye un nautilo, de estilo sketch y situado en el interior del antebrazo. Tattoo artist: Fabio Mauro

question: was there as much of a coherent ideology behind art deco as there was behind modernism? and if so what was it?

Art Deco is a style not an ideology like Modernism.

The term “Art Deco” comes from the Exposition Internationale des Arts Décoratifs et Industriels Modernes (International Exposition of Modern Industrial and Decorative Arts), the World’s fair held in Paris, France from April to October 1925. It was derived by shortening the words “Arts Décoratifs” in the title of the exposition.

Koch Snowflake: Finite area, Infinite perimeter.

The Koch Snowflake has finite area but infinite perimeter… yeah that happens with fractals. This abstract curve requires an infinite process (depicted in the gif) to construct and is an example of a fractal–a mathematical set (usually a curve or geometric figure) which exhibits a repeating pattern that displays at every scale. (More about fractals here https://en.wikipedia.org/wiki/Fractal)

But How? It seems clear that the area would be finite since the figure encloses a finite amount of space. To grasp why the Koch Snowflake has infinite perimeter, notice how as the iterations progress, the edges become more and more intricate. Now imagine trying to draw the edges with a pen. Since the construction of the snowflake continues indefinitely, the edges become infinitely intricate and you could never finish detailing these intricacies with your pen (that is the intuitive argument at least. I’ll leave the precise calculations up to you).

Fractals may seem so abstract and impractical but they actually have many useful real-world applications. For example, Benoit Mandelbrot (considered the “father of fractals”) found that stock market prices could be modeled with a factual curve. Check the wiki page for a long and diverse list of applications.

Fractal geometry may seem more abstract than traditional geometry but Mandelbrot argues that fractals are “the geometry of nature”. Objects in nature have random irregularities and are seemingly infinite in their intricacies. Attempting to incorporate this in drawings or animations is extremely difficult. Movie special effects and CGI often use fractals to make objects appear more natural looking. Since fractals can be made with mathematical formulae they are easy to generate with a computer. The first Star Wars movies were renowned for their special effects and were some of the first to use fractals to generate life-like explosions and landscapes of other worlds.

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Spirotechnics are related to two types of mathematical curves called hypotrochoids and epitrochoids, which are created by tracing the path of a point on one circle while it is rolled around the perimeter of another.

The distinction between the two is that hypotrochoids are created by rolling a circle inside a stationary circle, and epitrochoids are created by rolling a circle on the outside.

In Spirotechnics, multiple hypotrochoids and epitrochoids are nested within or outside each other, producing an endless variety of shapes.

ἄλογος  “not to be spoken”

## WEEK 2 [Day 5]

In Ancient Greeks, up until Greece fell to Rome, geometry was the main mathematical science. Scientists practiced geometry to explore the relationships among points, lines, angles, and shapes.

Numbers was their religion, they thought of numbers as simple, pure and elegant. Therefore, they only believed in whole numbers (i.e, 6, 14, etc.) and ratios that are made up of whole numbers (i.e, 8/9, 2/3, etc.).  If a value wasn’t whole, or couldn’t be represented as a ratio of whole numbers, then it wasn’t a true number to them.

Pointing out that geometry actually needed other kinds of numbers was a kind of blasphemy. Legend has it that a Mathematician named Hippasus was thrown from a ship, condemned to drown at the bottom of the sea, for having proved what was contrary to their belief: That numbers can be imperfect.

Later Greek scholars had to confront the reality of the faults in their beliefs. But rather than make room in their understanding for numbers that weren’t whole, or weren’t ratios of whole numbers, they instead decided that those numbers were “ἄλογος”, meaning both “not a ratio” and “not to be spoken.”

The “not a number” fallacy prevented Greek algebraists of the time from advancing. For them, numbers had to be spoken, or at least written out. They followed the Pythagorean rule because they were fearful of joining Hippasus at the bottom of the Mediterranean Sea.

I used the cover of “The Web Design Book Volume 5″ for the shapes

Infinite Growth

You play D&D? I seriously doubt that. I bet you don't even know what dice are.

Wait wait wait so you’re telling me

That these things aren’t elaborately shaped slightly mathematical candies?

I’m still gunna check

shit

So anyone else have an idea that the number 20 is important in the Bureau of Balance design scheme?

- The buildings are described as looking like geodesic domes;  possibly resembling icosahedrons; a kinda roundish shape made of triangles.

- The training arena is formally known as the Icosagon.

- The emblem of the Bureau resembles two X’s when turned on its side- 20 in Roman numerals.

-Probably a coincidence, but on the TAZ Wiki, exactly 20 named characters are listed as bureau members.

Even if unintentional, it still works very well symbolism-wise, as the d20 is arguably the most important piece in a D&D game. What’s more, the icosahedron shape is the Platonic solid (3D shape where all the planes have equilateral faces and the same angle between each face) with the most facets, and such a mathematically perfect shape would likely be symbolic of order.

Tell Me What You See #007 Mathematical Concepts Part_02

Visualizing sine (red) on the Y axis and cosine (blue) on the X axis. The relative position of the circle is shown in black:

This shows the same thing, but a bit more simply:

Here’s how sine and cosine apply to triangles:

Cosine is the derivative of sine:

Tangent lines:

Flipped on its side, the shape begins to make more sense:

Converting a function from Cartesian to Polar coordinates:

Drawing a parabola:

The Riemann sum is the approximate area under a curve:

Hyperbola:

Translating that into 3D, you get a hyperboloid. Believe it or not, it’s made with completely straight lines:

Seriously. You can even make it do this:

Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.
—  Benoit Mandelbrot, “On Smoothness,” c. 1990

I saw ur fidget collection and thought I'd point u to nanodots magnets! I have them and they are like the best fidget toys. U can make all sorts of mathematical shapes and just fun to smoosh!

OH HECK YEAH I put those on my wishlist just now, thank you so much!! I’d seen them before but had no idea what they were called!

relatable math feeling #3

the joy you feel when you realize a squircle is the name of a legitimate, recognized mathematical shape

# The Question That Could Unite Quantum Theory With General Relativity: Is Spacetime Countable?

Current thinking about quantum gravity assumes that spacetime exists in countable lumps, like grains of sand. That can’t be right, can it?

One of the big problems with quantum gravity is that it generates infinities that have no physical meaning. These come about because quantum mechanics implies that accurate measurements of the universe on the tiniest scales require high-energy. But when the scale becomes very small, the energy density associated with a measurement is so great that it should lead to the formation of a black hole, which would paradoxically ruin the measurement that created it.

These kinds of infinities are something of an annoyance. Their paradoxical nature makes them hard to deal with mathematically and difficult to reconcile with our knowledge of the universe, which as far as we can tell, avoids this kind of paradoxical behaviour.

The Ghost Zone’s Shape

Headcanon: the ghost zone is spirals within spirals.

The interaction of several small entities that make up something grander than the sum of its parts.

(source)

It looks like we’re actually going to be able to make our game work on the 3DS!****(probably!*****)

Having signed up for Nintendo development I’m not allowed to share information about systems and specs, so I won’t go into detail, but there are some aspects of 3DS development I want to share with you all:

Textures VS polygons

When I started working on graphics for this, I used Spyro as reference, and by extension the limits of the PS1. The Playstation’s main problem was its inability to render many polygons at the same time, so everything had to be extremely lowpoly and a lot of fancy trickery had to be used to make it look like there was more geometry on the screen than there actually was. On the other hand, the Playstation used big discs and had quite a bit of video memory, which allowed it to have many fairly big texture maps (for the time). The Nintendo 64 could hardly fit any textures at all, but used mipmapping instead, to “smudge out” the images, so that two pixels would be enough to make a perfectly smooth gradient. The N64 approach meant that geometry had to be used very cleverly to imply detail, since detail couldn’t really be stored in texturemaps. A lot of very tiny pixel-constellations were also used to create repeating patterns.