biology-and-math
mindblowingscience:

Top Math Prize Has Its First Female Winner

Image above: Winners of the 2014 Fields Medal in Mathematics, from left: Maryam Mirzakhani, Artur Avila, Manjul Bhargava and Martin Hairer. 
An Iranian mathematician is the first woman ever to receive a Fields Medal, often considered to be mathematics’ equivalent of the Nobel Prize.
The recipient, Maryam Mirzakhani, a professor at Stanford, was one of four scheduled to be honored on Wednesday at the International Congress of Mathematicians in Seoul, South Korea.
The Fields Medal is given every four years, and several can be awarded at once. The other recipients this year are: Artur Avila of the National Institute of Pure and Applied Mathematics in Brazil and the National Center for Scientific Research in France; Manjul Bhargava of Princeton University; and Martin Hairer of the University of Warwick in England.
The 52 medalists from previous years were all men.
"This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Dr. Mirzakhani was quoted as saying in a Stanford news release on Tuesday. "I am sure there will be many more women winning this kind of award in coming years."

Continue Reading.

mindblowingscience:

Top Math Prize Has Its First Female Winner

Image above: Winners of the 2014 Fields Medal in Mathematics, from left: Maryam Mirzakhani, Artur Avila, Manjul Bhargava and Martin Hairer. 

An Iranian mathematician is the first woman ever to receive a Fields Medal, often considered to be mathematics’ equivalent of the Nobel Prize.

The recipient, Maryam Mirzakhani, a professor at Stanford, was one of four scheduled to be honored on Wednesday at the International Congress of Mathematicians in Seoul, South Korea.

The Fields Medal is given every four years, and several can be awarded at once. The other recipients this year are: Artur Avila of the National Institute of Pure and Applied Mathematics in Brazil and the National Center for Scientific Research in France; Manjul Bhargava of Princeton University; and Martin Hairer of the University of Warwick in England.

The 52 medalists from previous years were all men.

"This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Dr. Mirzakhani was quoted as saying in a Stanford news release on Tuesday. "I am sure there will be many more women winning this kind of award in coming years."

Continue Reading.

Anonymous asked:

hi... could you help me with something? what do those numbers and letters on a car's gear shift/stick mean?

Hello, 

Sorry but I haven’t really got a good idea of what they are myself, I don’t drive and I never really paid too much attention to things like this. 

I think though that the numbers are probably gears that increase the maximum cap of the speed the car can go at as the numbers increase. (This is a complete and utter guess.) 

The letters, if I remember are: P, R, N, D, L 

P - Park, used when you want to park the car I assume 

R - Reverse, alters the rotation of the wheels so that the car moves backwards. 

N - Neutral, not 100% what this means. Not even 5% sure what this means sorry. 

D - Drive, also no idea what this means, sorry. 

L - Low, I think this means that this is used when going up a hill? I don’t know. 

I’m not much of a car person… Sorry

mathed-potatoes

drawingsheep:

visualizingmath:

Cubes fall through “Flatland”. On the left is a view of the cube in perspective; on the right is a view from directly above which represents what a two-dimensional person viewing the cube from within the plane would be able to perceive.

The top animation shows a square falling through flatland on its face. The slices are always squares. So our two-dimensional person would see “a square existing for a while”.

The second animation shows a square falling through flatland on one of its edges. The slice begins as an edge, then becomes a rectangle; the rectangle grows, becomes a square for a moment, and then gets wider than it is tall. At its widest, it is as wide as the diagonal of one of the square faces of the cube. The rectangle then shrinks back to an edge at the top of the cube.

The third animation is the coolest one! The cube passes through Flatland on one of its corners. In this case, the initial contact is a point, which then becomes a small equilateral triangle. This triangle grows until it touches three of the corners of the cube. At this point, the corners of the triangles begin to be cut off by the other three faces of the cube. For a short moment, the triangle turns into a certain regular polygon..As the cube progresses through the plane, the slice turns again into a cut-off triangle (but inverted with respect to the original one) and finally becomes an equilateral triangle once again as three more vertices pass through the plane. This triangle shrinks down to a point and disappears.

In the third animation, what regular polygon does the triangle turn into halfway through its fall? If you can’t figure out, maybe this artwork by Robert Fathauer will help. (Scroll to the bottom.)

If a 4D cube entered our dimension, what would we see? If you can’t figure this out, check out this awesome page. (Click the GIF links.)

If you haven’t read Flatland, read it! Fascinating little book.

I have never stopped being amazed by the fact that you can make a hexagon by dropping a cube through a 2-dimensional plane. 

instagral

okkultmotionpictures:

EXCERPTS >|< Journey to the Center of a Triangle (1976)


 | Hosted at: Internet Archive
 | From: Academic Film Archive of North America
 | Download: Ogg | 512Kb MPEG4 | MPEG2
 | Digital Copy: not specified


A series of Animated GIFs excerpted from Journey to the Center of a Triangle (1977): another fabulous film by the Cornwells, created on the Tektronics 4051 Graphics Terminal. Presents a series of animated constructions that determine the center of a variety of triangles, including such centers as circumcenter, incenter, centroid and orthocenter. More on the Cornwells at http://www.afana.org/cornwell.htm

According to son Eric Cornwell, here’s how the film was made: The 4051 produced only black and green vector images, not even grey scale. The film’s scenes were divided into layers in the programming, one layer for each of the colors in the scene, and each was shot separately onto high-contrast fine-grained b&w film stock. The final scene in “Journey” had 5 layers: one for each of the four colored dots, plus one for the white triangle and line. 

These five clips were then multiple-exposed onto color film on an optical printer, using colored filters to add the desired color to each black&white layer as it was copied. The resulting color was much better than a film of an RGB display would have been because the color filters on the optical printer allowed access to the full range of the color negative film, allowing much more saturated colors. All of that color is pretty much lost now, between prints fading and/or transfers to the VHS, and then viewing them on a computer screen which has a much more limited color gamut. Please imagine it all in bright, brilliant colors. (from Internet Archive)

We invite you to watch the full video HERE.




EXCERPTS by OKKULT Motion Pictures: a collection of GIFs excerpted from out-of-copyright/historical/rare/controversial moving images. 
A digital curation project for the diffusion of open knowledge.

>|<

shychemist
fathom-the-universe:

The tesseract. A tesseract is the four dimensional analogue of the cube.The cube is to the tesseract what the square is to the cube. The cube has a surface composed of six faces (squares). A tesseract has a hypersurface composed of eight cells (cubes) and is also called an octachoron or 8-cell. You can also call a tesseract a hypercube. The prefix hyper- simply means it has more than three dimensions. You can also have 5D hypercube.Of course we cannot physically construct a tesseract in four dimensions, but we can create a projection in two or three dimensions,If you want to draw a tesseract, connect the vertices of two cubes. Compare it to the drawing of a cube, where you connect the vertices of two squares. Remember that you are only looking at a lower dimensional “shadow” of a tesseract. All cubes in the tesseract are the same size. The cube in the centre appears smaller because it is further away in four dimensions.

Fathom the Universe

fathom-the-universe:

The tesseract. 

A tesseract is the four dimensional analogue of the cube.
The cube is to the tesseract what the square is to the cube. 
The cube has a surface composed of six faces (squares). 
A tesseract has a hypersurface composed of eight cells (cubes) and is also called an octachoron or 8-cell. 
You can also call a tesseract a hypercube. The prefix hyper- simply means it has more than three dimensions. You can also have 5D hypercube.
Of course we cannot physically construct a tesseract in four dimensions, but we can create a projection in two or three dimensions,

If you want to draw a tesseract, connect the vertices of two cubes. Compare it to the drawing of a cube, where you connect the vertices of two squares. 
Remember that you are only looking at a lower dimensional “shadow” of a tesseract. All cubes in the tesseract are the same size. The cube in the centre appears smaller because it is further away in four dimensions.

Fathom the Universe

This one time I was at a party and there was a lamp that kind of did the thing so it looked like a tesseract (not the Avengers thing, the 4 dimensional object) and a friend pointed it out to me then challenged me to make a pick up line out of it. 

So I grabbed the nearest girl, asked her to sit down with me and I said: 

"Look at this, this is a 4 dimensional tesseract, only it’s not. It’s a 2 dimensional image frame that we are seeing of a 3 dimensional object in our 3 dimensional world, that perfectly illustrates one viewing angle of this regular 4 dimensional object. Isn’t that amazing? I think it’s pretty beautiful how something like this is possible, and it’s even more beautiful that even if we were to rotate the tesseract through the 4 dimensions, we could still have a representation of it one and two dimensions lower. I’m sure if we could see in 4 dimensions, that if we occupied a 4 dimensional world we’d be better equipped to witness the beauty of the tesseract, but even so this is still stunningly amazing, don’t you think?" 

At this point she’s nodding, moderately impressed, so I looked her over and continued with: 

"Hey, can I ask you something? Are you a tesseract?" 

And I swear no one has ever or will ever laugh at me that hard ever again. 

(I don’t even think half of what I said was accurate at all). 

ngeetee asked:

How does Gabriel's horn have finite volume? Wouldnt the radius just get infinitely smaller but never reach zero?

ngeetee

Gabriel’s Horn has infinite length which is important because “at infinity” (a term that I have been told off multiple times for using but that I feel gets the point across nicely) the radius will have reached zero as it is continuously tending towards zero. 

Using a bit of calculus we can calculate the volume of the horn which shows us that the horn has finite volume. 

Gabriel’s Horn is a shape created by rotating the graph of y=1/x about the x-axis for x>= 1.

Imagine the bit of the graph of y=1/x and then rotating that through 360 degrees around the x-axis, such that it carves out a 3-dimensional object. This is Gabriel’s Horn.

From this we see that the radius of Gabriel’s Horn along the x-axis is equivalent to y, and hence r=1/x.

We can calculate the surface area and volume of Gabriel’s Horn by taking integrating between x=1 and infinity the expressions for the circumference and cross-sectional area of Gabriel’s Horn respectively. As the cross section is simply a circle at each point, the expressions required are 2πr and πr^2.

Hence the volume is given by π times the integral of y^2 = 1/(x^2) with respect to x from x=1 to infinity.

By taking the integral of 1/(x^2) with respect to x from x=1 to a, we see that the volume of Gabriel’s Horn between x=1 and a is (-1/a) – (-1/1) = 1 - 1/a = (a-1)/a. As a approaches infinity, (a-1)/a approaches 1 and thus the volume of Gabriel’s Horn is π*1 = π

The surface area is therefore given as 2π times the integral of y= 1/x with respect to x between x=1 and infinity.

Once more, taking the integral of 1/x with respect to x from x = 1 to x = a and tending a to infinity, we get ln(a) – ln(1) = ln(a). However, ln(x) is an increasing function, and so as a tends to infinity so does ln(a), meaning that the surface area of Gabriel’s Horn is infinite.

And so we have that the surface area of Gabriel’s Horn is infinite, whereas the volume is finite.

Hope this has helped clear things up! Have a nice day.