mathblab:

jiajia-binks:

mathblab:

mathblab:

IMPOSSIBLE! Right? You may have heard “the interior angles of a triangle always add up to 180 degrees”. This is not always true. Check out the second image, it shows a triangle with 3 right angles for a total of 270 degrees! 

It is true in flat Euclidean geometry (the geometry you probably learned in school) however. But there are so many other geometries out there! You may be thinking, are other geometries real though? A mathematician would argue they are just as real as the typical flat geometry you know and love (or hate). These alternative geometries can be practically useful too!

The images above show triangles in spherical geometry. Those aren’t triangles though! Oh but they are! A triangle is just a polygon enclosed by three lines. Looks like it fits the criteria. Wait but those aren’t lines, they are curved! Ah yes. I argue that these are, for all intents and purposes, just as good as lines. We need to ask: What is a line? A line is so basic to us we may not know how to describe it. I offer this definition: A line is the shortest path between 2 points. The 3 curves that make the triangle above are in fact the shortest paths from one vertex to the other on the surface of the sphere (they just so happen to be on circumferences of the sphere, which are often referred to as great circles). So it may be more useful to think of lines, in general, as length minimizing curves. In conclusion, we would consider the shape above to be a triangle as it is enclosed by 3 length minimizing curves on a surface.

Spherical geometry can be very useful; think about the Earth. To reduce travel time, airplanes would want to travel along great circles as they are the shortest paths from one place to another. Additionally, this type of thinking (rethinking straight lines as length minimizing curves) is central to Albert Einstein’s general theory of relativity.

read more at http://staffrm.io/@missnorledge/35H6cS1T52

You must unlearn what you have learned. — Yoda

In my eyes, art is something that expresses or represents the artist’s interpretation of a subject. Painters create paintings to represent what they see or imagine. Mathematicians use math to express how they interpret phenomenon in the real world. 

For example, Albert Einstein was able to convey his imaginative theories through the language of mathematics. His theories and following conclusions revolutionized the way we perceive the world. Abstract concepts like space-time and the equivalence of mass and energy were proven through Einstein’s mathematical calculations. The picture and explanation above are related to Einstein’s general theory of relativity. His theory involves rethinking what we believe are “straight lines” and “flat planes”. Mathematicians developed alternative geometries, like spherical geometry, in order to create a new medium in which to interpret characteristics of the universe in. We have been able to perform calculations and make new discoveries about curved space using alternative geometry. This innovation is an example of mathematic’s potential for imaginative expansion. The artistry in this lies in the creative processes required to achieve understanding of our world and the expression of one’s ideas through math.

Others may define art as something that is aesthetically pleasing or simply just beautiful. I concede that not all people may find equations pleasing at first, but I believe that equations can have a unique kind of beauty if you even just have a slight understanding of what it represents. There is a certain elegance in the simplicity of Einstein’s most famous equation, E=mc², especially since it encompasses energy and matter, the two things that make up the entire universe as we understand it. It is beautiful that we can create a theory or model of anything in the language of mathematics.

Yes I agree. I get the feeling, from several mathematicians I know, that they do seem to approach mathematics from an artistic point of view. 

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firellily:

riderluk:

tayloracleswift:

“I’m so fly I’ve got arachnophobia” holy shit

damn son

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the-rogue-apostate:

Oh my god

Originally posted by cutepetplanet

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