thefatgirlblog:

"All these young girls getting themselves pregnant"

Wow, self impregnating teenage girls, these men should be afraid, we as woman are evolving at alarming rates.

wasbella102:

Study. Sky after sunset. Hudson River School.

wasbella102:

Study. Sky after sunset. Hudson River School.

xysciences:

Sine, Cosine, and the resulting unit circle. 

xysciences:

Sine, Cosine, and the resulting unit circle. 

1ucasvb:

The familiar trigonometric functions can be geometrically derived from a circle.

But what if, instead of the circle, we used a regular polygon?

In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1.

We’ll keep using the angle from the x-axis as the function’s input, instead of the distance along the shape’s boundary. (These are only the same value in the case of a unit circle!) This is why the square does not trace a straight diagonal line, as you might expect, but a segment of the tangent function. In other words, the speed of the dot around the polygon is not constant anymore, but the angle the dot makes changes at a constant rate. 

Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon.

More on this subject and derivations of the functions can be found in this other post

Now you can also listen to what these waves sound like.

This technique is general for any polar curve. Here’s a heart’s sine function, for instance

1ucasvb:

The familiar trigonometric functions can be geometrically derived from a circle.

But what if, instead of the circle, we used a regular polygon?

In this animation, we see what the “polygonal sine” looks like for the square and the hexagon. The polygon is such that the inscribed circle has radius 1.

We’ll keep using the angle from the x-axis as the function’s input, instead of the distance along the shape’s boundary. (These are only the same value in the case of a unit circle!) This is why the square does not trace a straight diagonal line, as you might expect, but a segment of the tangent function. In other words, the speed of the dot around the polygon is not constant anymore, but the angle the dot makes changes at a constant rate.

Since these polygons are not perfectly symmetrical like the circle, the function will depend on the orientation of the polygon.

More on this subject and derivations of the functions can be found in this other post

Now you can also listen to what these waves sound like.

This technique is general for any polar curve. Here’s a heart’s sine function, for instance

red-lipstick:

Wittap aka Witta Priester (New Zealand) - Canterbury Arch or Asperatus Cloud?, 2005  An amazing sky taken off the deck of a rental home in Hanmer, NZ.      Photography

red-lipstick:

Wittap aka Witta Priester (New Zealand) - Canterbury Arch or Asperatus Cloud?, 2005  An amazing sky taken off the deck of a rental home in Hanmer, NZ.      Photography

coltre:

With both her parents being nature photographers, Tippi Degre has had one amazing childhood. Before she was born, her French parents relocated to Namibia, Africa, where she grew up alongside wild animals such as zebras, elephants, cheetahs, and lions. During her stay in Namibia, she befriended a 28-year old elephant named Abu.

coltre:

With both her parents being nature photographers, Tippi Degre has had one amazing childhood. Before she was born, her French parents relocated to Namibia, Africa, where she grew up alongside wild animals such as zebras, elephants, cheetahs, and lions. During her stay in Namibia, she befriended a 28-year old elephant named Abu.

workman:

sosuperawesome:

Small and miniature oil paintings by Jessica Gardner

trafial:

cloudy, Tomasz Trafiał tome

trafial:

cloudy, Tomasz Trafiał tome

Paul Delaroche - The Young Martyr (1855)

hotidiot:

spectacularuniverse:

Sphaerodactylus nicholsi, one of the smallest geckos in the planet. (x)

This is amazing. Look how small it is. It has a heart and a stomach and a brain. And it’s this small

hotidiot:

spectacularuniverse:

Sphaerodactylus nicholsi, one of the smallest geckos in the planet. (x)

This is amazing. Look how small it is. It has a heart and a stomach and a brain. And it’s this small

cryinodonoghue:

theres a grief that cant be spoken

theres a pain goes on and on

empty chairs at empty tables

im not going to comic con