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Mathmajik

Thinking Too Much
Sep 27 '14

(Source: patakk)

Sep 27 '14

ryanandmath:

I stumbled across a game called Vax, which lets you simulate an epidemic breakout in a very graph-theoretic mindset. You only have two tools though: you can either vaccinate an infected vertex or you can cut out a vertex altogether. And that notion reminded me of this quote I had read sometime ago, in particular:

Take the web of interactions within a cell. If you knock out an important gene, you will significantly damage the cell’s growth rate. However, it is possible to repair this damage not by replacing the lost gene, which is a very challenging task, but by removing additional genes.

The key lies in finding the specific changes that would bring a network from the undesirable state A to the preferred state B.

So although this seems like a simple problem at first glance, you can actually apply some pretty sophisticated mathematics to try and optimize how you can control your infected system. If you’re mathematically savvy, trying checking out the paper in which they look at how you can understand these types of situations

Sep 24 '14
Sep 24 '14
Sep 24 '14
Sep 22 '14

Fascinated by the intricate patterns formed by fractals, basically math processes that repeat incessantly in an ongoing feedback loop, UK physicist-turned-web developer Tom Beddard makes impossibly elaborate complexes that look like they belong in the gritty cities of a dystopian fantasy. Basically what he does is write and run programs on his computer that spit out patterns—”the best outcomes are often the least expected!” he writes—that he in turn massages (by way of shadowing and the like) into looking like faceted steel-and-concrete architecture.
Sources:
Curbed.com
Architizer.com

Sep 22 '14
What makes the Julia Necklace, courtesy of Mark Newson and Boucheron, a unique, “insolent and audacious” (Boucheron’s description) is the illustrious inspiration it embodies: a blend of fine artistry, craftsmanship and mathematics. Newson’s timely and constant passion for fractals has found an expression in the design of the Julia Necklace. The necklace is a representation of Julia fractals (named after the scientist who discovered them, Julia Gaston), discovered at the dawn of the twentieth century. For the reader to make a general idea: fractals are rough geometrical shape which can be divided and subdivided endlessly in other units almost identical to them.

      In spite of its impressive dimensions this piece of jewelry is not heavy or difficult to wear. Its manufacturing has probably been a blood and tears job, with the jewelers’ ambition to go by the book on representing the accurate mathematic representation of each fractal. Nevertheless, what is most important is the astonishing result which can be truly added to the world’s timeless jewelry legacy.

      The Julia necklace was not intended to be a costly piece, as Newson declared, but its time, craftsmanship and minute detail requirements will probably transform it in one of Boucheron’s most expensive pieces.

http://www.jewelrycollection.eu/boucheron/

What makes the Julia Necklace, courtesy of Mark Newson and Boucheron, a unique, “insolent and audacious” (Boucheron’s description) is the illustrious inspiration it embodies: a blend of fine artistry, craftsmanship and mathematics. Newson’s timely and constant passion for fractals has found an expression in the design of the Julia Necklace. The necklace is a representation of Julia fractals (named after the scientist who discovered them, Julia Gaston), discovered at the dawn of the twentieth century. For the reader to make a general idea: fractals are rough geometrical shape which can be divided and subdivided endlessly in other units almost identical to them.

In spite of its impressive dimensions this piece of jewelry is not heavy or difficult to wear. Its manufacturing has probably been a blood and tears job, with the jewelers’ ambition to go by the book on representing the accurate mathematic representation of each fractal. Nevertheless, what is most important is the astonishing result which can be truly added to the world’s timeless jewelry legacy.

The Julia necklace was not intended to be a costly piece, as Newson declared, but its time, craftsmanship and minute detail requirements will probably transform it in one of Boucheron’s most expensive pieces.

http://www.jewelrycollection.eu/boucheron/

Sep 22 '14

Spring Forest (5,3): embedded, unembedded, and cowl
12” x 11” x 9”
Knitted wool (Dream in Color Classy, in colors Happy Forest and Spring Tickle)
2009 and 2013
A (p,q) torus knot traverses the meridian cycle of a torus p times and the longitudinal cycle q times. Here are three instantiations of a (5,3) torus knot:
(a, middle) The knot embedded on a torus. A (p,q) torus knot may be drawn on a standard flat torus as a line of slope q/p. The challenge is to design a thickened line with constant slope on a curved surface.
(b, top) The knot projection knitted with a neighborhood of the embedding torus. The knitting proceeds meridianwise, as opposed to the embedded knot, which is knitted longitudinally. Here, one must form the knitting needle into a (5,3) torus knot prior to working rounds.
(c, bottom) The knot projection knitted into a cowl. The result looks like a skinny knotted torus.

Modern Striped Klein
2” x 14” x 7”
Knitted wool (Dream in Color Classy Firescorched in Aqua Jet with Sundown Orchid and Happy Forest)
2013
This Klein bottle was knitted from an intrinsic-twist Mobius band with the boundary self-identified. A Klein bottle can be viewed as the connected sum of two projective planes; here, the stripes highlight the two circles that generate the fundamental groups of the individual projective planes. In some positions, this coloring of the Klein bottle resembles an ouroboros (a snake eating its own tail). The design is more than 10 years old; I recently realized that I had no high-quality example of it (only worn classroom models) and thus created one. Dream in Color veil-dyed yarn was chosen to add a color depth to the seed-stitch texture. Images of this piece graced the cover of the March-April 2013 issue of American Scientist.

Free-Range Mathematician
Sarah Lawrence College / Smith College
Hadley, MA
http://www.toroidalsnark.net

Sep 20 '14
d3lt4:

"Fiboncci Sequence (Square)" Art print
Leonardo Fibonacci is an Italian mathematician from the 12th century.

d3lt4:

"Fiboncci Sequence (Square)" Art print

Leonardo Fibonacci is an Italian mathematician from the 12th century.

Sep 20 '14

sciencesourceimages:

How Mandelbrot’s Fractals Changed The World

by Jack Challoner/BBC News

During the 1980s, people became familiar with fractals through those weird, colorful patterns made by computers. But few realize how the idea of fractals has revolutionized our understanding of the world, and how many fractal-based systems we depend upon.

Unfortunately, there is no definition of fractals that is both simple and accurate. Like so many things in modern science and mathematics, discussions of “fractal geometry” can quickly go over the heads of the non-mathematically-minded. This is a real shame, because there is profound beauty and power in the idea of fractals.

The best way to get a feeling for what fractals are is to consider some examples. Clouds, mountains, coastlines, cauliflowers and ferns are all natural fractals. These shapes have something in common - something intuitive, accessible and aesthetic.

They are all complicated and irregular: the sort of shape that mathematicians used to shy away from in favor of regular ones, like spheres, which they could tame with equations.

Mandelbrot famously wrote: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

The chaos and irregularity of the world - Mandelbrot referred to it as “roughness” - is something to be celebrated. It would be a shame if clouds really were spheres, and mountains cones.

Look closely at a fractal, and you will find that the complexity is still present at a smaller scale. A small cloud is strikingly similar to the whole thing. A pine tree is composed of branches that are composed of branches - which in turn are composed of branches.

Read the entire article

Fractal images © Laguna Design / Science Source

Mandelbrodt photo © Emilio Segrè / Science Source

Sep 20 '14
antarctica246:

Sacred Tree on Flickr.Via Flickr:
ChaosPro

antarctica246:

Sacred Tree on Flickr.

Via Flickr:
ChaosPro

Sep 20 '14
megustadisto:

One of The #best #jokes about #math ||  #pirates and #Stuff || AAARRRRRGGGG

megustadisto:

One of The #best #jokes about #math || #pirates and #Stuff || AAARRRRRGGGG

Sep 12 '14
dumb-science-jokes:

trigonometry-is-my-bitch:

"Glassified" Ruler by MIT Media Lab Automatically Measures Angles, Volume, and Shape Properties.
[source]


Will that ever be a practical device

dumb-science-jokes:

trigonometry-is-my-bitch:

"Glassified" Ruler by MIT Media Lab Automatically Measures Angles, Volume, and Shape Properties.

[source]

Will that ever be a practical device

Aug 26 '14

(Source: bassistdrix)

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