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# Doodling in math: Connecting dots

Anti-parabola propoganda, plus musing on math class, cardioids, connect the dots, envelopes of lines, even a bit of origami.Extra points to a certain Andrea whose line-enveloped Hilbert curve inspired me to finish this video. Created by Vi Hart.

## Want to join the conversation?

• so does this mean that on a sphere a parabola cant happen
• Interesting question. Given what Vi is saying here, the thing that makes a parabola is that point at infinity. We've stretched out our ellipse so that our second focus is at the point at infinity, which means it's open. However, if we are working on a sphere, we always end up meeting around the other side. Let's take a lesson from Vi and try this ourselves. Take a ball and see what happens when you draw a parabola shape and don't just stop.
• At , Vi says that the cardioid is like an "Anti-parabola", and I don't quite understand what that mean. Please explain.
• If you turn positive to negative, infinity to zero while graphing a parabola you get a cardioid
• Is there a way to get my calculator to graph the cardioid?
I've tried all sorts of stuff with x^2 but it just comes up with other very strange graphs.
• The equation I found is (x^2+y^2+ab)^2=a^2(x^2+y^2), where a is any real number and b is equal to x or y. (Use y to get the up-down cartioid)
• so let me get this strait a cardioid is the anti parabola because loads of parabolas rotated? i am confused can someone explain?
• If you invert the parabola you get a cardioid
• Thoroughout the entire video, I was wondering "what is an anti-parabola?" Is it a movement that suggests parabolas should not be the main focus of Conic Sections? Or, is an anti-parabola a specific, mathematical term for something?
• No. Vi is refering to the cardioid. Parabolas have two focus points a (any real number) and infinity. If you turn inifinity into 0, you have a cardioid. Hope this helps!
• how did you get the cool heart i,m still trying to figure it out.
• If you like programming this may help.

Otherwise the best instructions I can give are draw a circle and some evenly spaced points on that circle. Next assign one point to be on the edge of all future circles and finally draw a circle centerd on each point.