Solar System: Things To Know This Week

Guise …

In “taxicab geometry”, circles are square-shaped. Wait … circles and squares are different shapes. Yes, this is true, but mathematically, a circle does not have to be circle-shaped. To see this, we need look at the definition of a circle and consider unusual geometries. There are other geometries? Yup!

In all geometries, the definition of a circle is the same: a circle is the collection of all points some fixed distance from a fixed center. In taxicab geometry, distance is strange (above left) so circles are too. A taxi can only drive on streets so distance from one point to another is calculated considering the shortest possible path to take along the streets not necessarily the straight line distance from point A to point B. In taxicab geometry, the only points that exist are points on a grid and 1 unit of distance is one city block.

On the right are examples of circles in taxicab geometry. The top one, for example, represents all the points 2 blocks away from the center blue point (and hence a circle of radius 2). As we can see these circles end up being square-shaped!

All this may seem like just fun and games but these ideas have a deep mathematical significance. In the area of mathematical analysis, taxicab geometry has connections to L^p spaces.

For more info see https://en.wikipedia.org/wiki/Taxicab_geometry

I hate that so many places will automatically convert :P into 

like what is that. That’s not what I wanted to convey at all. 

:P means

.

LG is the only company that gets it at all 

Thank you for your service, LG. You alone understand. My apologies to anyone using your service who tries to sent this to anyone using any of the other services.

God ok FINE….roll to seduce the sword

(via outofcontextdnd)

Out of Nothing, I have created a strange new universe.

János Bolyai, speaking of his discovery of a non-Euclidean geometry. (via mathblab)

CIRCLE SQUARE GEOMETRY

Here is an example of AREA of geometry without using numbers or math, it is purely visual. It compares a  SQUARE and CIRCLE and sees how their areas relate to one another.

Lesser-known small wild cats photographed by Joel Sartore 1. Margay 2. Jaguarundi 3. Black-footed Cat 4. Fishing Cat 5. Flat-headed Cat 6. Leopard Cat 7. Sand Cat 8. Geoffroy’s Cat 9. Rusty Spotted Cat 10. African Golden Cat

Unit circle.

Perspective matters