Brief lecture on hyperbolas.

Musicvideo of Aldo Tamarinds song "Hyperbola View", created by Vera Vermon Minimal Techno

I created this video using my Logitech QuickCam software

Funny Math project.

Showing the familiar reflection property of the hyperbola - using both rays and wave fronts. For more information, films, and interactive material, see http://tinyurl.com/3wgcsa

Hyperbola: General Form to Standard Form

Using the Table method to draw a hyperbola that shifted to the left

Hyperbola: Information for Graphing

This is a video showing Hyperbola CTF for Jedi Knight: Dark Forces II. The level was created by me as part of my Dralloc Series. It is the second CTF installation in the Dralloc CTF Trilogy, and is the ninth consecutive level in the entire Dralloc Series. This is just a stupid lil video featuring some of my online buddies. Gnarly, ZeqMacaw, JKLE_Cougar, and Kirby... the hacker. We got our asses handed to us as you might notice. The other team had all the good players except me. I had the newbs on my team. Doesn't matter though... it was still fun... even though kirby hax.

I created this video using my Logitech QuickCam software

straddle ball full up cupie

Hyperbola from Info

My great movie.

I created this video using my Logitech QuickCam software

trig coaster

The product of the distance from the green point (a vertex point of the hyperbola) to the blue point (on the hyperbola) and the distance from the green point to the red point (on the inverse curve) is constant (and equal to the square of the radius of the green circle). For more information, films, and interactive material, see http://tinyurl.com/62yuqc

The one-parameter family of curves that have the same normal lines as the hyperbola. For more information, films, and interactive material, see http://tinyurl.com/6ehctv

The product of the distance from the green point (the center the hyperbola) to the blue point (on the hyperbola) and the distance from the green point to the red point (on the inverse curve) is constant (and equal to the square of the radius of the green circle). For more information, films, and interactive material, see http://tinyurl.com/62yuqc

The product of the distance from the green point (a focal point of the hyperbola) to the blue point (on the hyperbola) and the distance from the green point to the red point (on the inverse curve) is constant (and equal to the square of the radius of the green circle). For more information, films, and interactive material, see http://tinyurl.com/62yuqc

The radial of a curve is constructed by parallel transport of the radius-vector of curvature of the given curve to a fixed point. For more information, films, and interactive material, see http://tinyurl.com/5g79v9

The positive pedal of a hyperbola with respect to its centre point is a lemniscate with the same centre point, and which touched the hyperbola at its vertices. For more information, films, and interactive material, see http://tinyurl.com/3lqhyy

The positive pedal of a hyperbola with respect to one of its focal points is a circle. For more information, films, and interactive material, see http://tinyurl.com/3lqhyy

The evolute of a hyperbola. For more information, films, and interactive material, see http://tinyurl.com/4lsylq

The projective plane is the space of lines through the origin in 3-space. In the projective plane, we have the remarkable fact that any two distinct lines meet in a unique point. Moreover, we may not distinquish between different kinds of smooth conic sections, e.g. between an ellipse and a hyperbola, as illustrated by the animation. Notice that to each line through the origin correspond two antipodal points of a sphere which is centered at the origin. Instead of looking at the lines in total, we may thus restrict ourselves to the points on the sphere. Here, a line becomes a great circle and it is clear that any two such circles meet in a unique pair of antipodal points. Similarly, we may see that a hyperbola is projectively the same thing as an ellipse. Going back to the definition: They are both just a cone in 3-space; each line on the cone is one projective point of the projective conic section. This animation was made by Oliver Labs using surfex. This animation was #3 on our geometric animations advent calendar: http://www.calendar.algebraicsurface.net

Showing the familiar reflection property of the hyperbola - using rays. For more information, films, and interactive material, see http://tinyurl.com/3wgcsa