forgive me father trigonometry, for i have sined
Versine.
The versine or versed sine, versin(θ), is a trigonometric function equal to 1 − cos(θ) and 2sin2(½θ). It appeared in some of the earliest trigonometric tables and was once widespread, but it is now little-used. There are several related functions, most notably the haversine, half the versine, known in the haversine formula of navigation.
It is also written as vers(θ) or ver(θ). In Latin, it is known as the sinus versus (flipped sine) or the sagitta (arrow).
y = versine(θ)
Found this on Tumblr a while ago. Didn’t reblog and subsequently lost it. Glad to have finally found it again!
Photographer Loves Math, Graphs Her Images
Here are some of the pictures the photographer named Nikki Graziano have captured. Graziano, is a math and photography student at Rochester Institute of Technology, she overlays graphs and their corresponding equations onto her carefully composed photos.
“I wanted to create something that could communicate how awesome math is, to everyone,” she says.
Graziano doesn’t go out looking for a specific function but lets one find her instead. Once she’s got an image she likes, Graziano whips up the numbers and tweaks the function until the graph it describes aligns perfectly with the photograph. See more of her Found Functions series at Nikkigraziano.com.
Neat graphical representation of how each of the trig functions of an angleθ corresponds to measurements on the unit circle.
The beauty of mathematics and numbers - through Euler’s identity, which ties together the imaginary number, the exponential, pi, 1 and 0. The imaginary number is derived out of necessity in algebra. The exponential number was invented for calculus for logarithmic and exponential functions, pi is essential in tying together geometry, and 1 and 0 are……well, everything. This equation ties together algebra, calculus, geometry, and basic numerology. And it was DISCOVERED. Not invented. That should say something, about the nature of numbers and math to who we are. Math has an unreasonable amount of utility in this universe, especially for something that we essentially INVENTED out of our own heads. It should tell us that there are connections out there that we might not even be aware of. That have not yet been discovered. How incredibly little we know about the world and universe we inhabit.
