CIRCLE SQUARE GEOMETRY

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

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

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

God ok FINE….roll to seduce the sword

(via outofcontextdnd)

Unit circle.

Perspective matters

Solar System: Things to Know This Week

Learn more about our Deep Space Network, where to watch the Ursid meteor shower, Cassini’s ring-grazing at Saturn and more.

1. A Deep Space Anniversary

On Dec. 24, 1963, the Jet Propulsion Laboratory’s Deep Space Information Facility was renamed the Deep Space Network. And, it’s been humanity’s ear to the skies ever since.

+ History of the Deep Space Network 

2. Ursid Meteor Shower 

The best time to view the Ursids, radiating from Ursa Minor, or the little Dipper, will be from midnight on December 21 until about 1a.m. on December 22, before the moon rises.

3. At Saturn, the Ring-Grazing Continues

Our Cassini spacecraft has completed several orbits that take it just outside Saturn’s famous rings. The first ring-grazing orbit began on November 30. The spacecraft will repeat this feat 20 times, with only about a week between each ring-plane crossing.

+ Learn more

4. Preparing for the 2017 Total Solar Eclipse

Next year North America will see one of the most rare and spectacular of all sky events. Learn how to prepare.

+ 2017 Solar Eclipse Toolkit

5. Searching for Rare Asteroids

Our first mission to return an asteroid sample to Earth will be multitasking during its two-year outbound cruise to the asteroid Bennu. On February 9-20, OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer) will activate its onboard camera suite and begin its search for elusive “Trojan,” asteroids, constant companions to planets in our solar system as they orbit the sun, remaining near a stable point 60 degrees in front of or behind the planet. Because they constantly lead or follow in the same orbit, they will never collide with their companion planet.

Discover the full list of 10 things to know about our solar system this week HERE.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com

Reblog the nat 1 garbage pile for just one session where your players don’t try to pull some half-baked gazebo bullshit

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

“ In mathematics, the mountain climbing problem is a problem of finding the conditions that two function forming profiles of a two-dimensional mountain must satisfy, so that two climbers can start on the bottom on the opposite sides of the mountain and coordinate their movements to reach to the top while always staying at the same height. “ Via Wikipedia.