# I ♥ Cardioids

August 31, 2012 10:22 AM Subscribe

I ♥ Cardioids, Vi Hart's condensed awesome tackles parabolas, cardioids, circles and more. Related: Part 1 of Rolling Circles and Balls.

She's totally my favorite person on YouTube, but I wish she'd slow her speech down just a

posted by Malor at 11:01 AM on August 31, 2012

*little*.posted by Malor at 11:01 AM on August 31, 2012

*I wish she'd slow her speech down just a little.*

She talks faster than that in person!

posted by Sidhedevil at 11:08 AM on August 31, 2012

I....

I have fallen in love.

Must go get graph paper and pencil now.

posted by mule98J at 11:14 AM on August 31, 2012

I have fallen in love.

Must go get graph paper and pencil now.

posted by mule98J at 11:14 AM on August 31, 2012

What I love about cardioids is how come they're the polar response patterns for microphones. Essentially, it's what you get when you add an omni (circle) response and a figure-of-eight response - i.e. a closed-back and free-diaphragm mic. If that seems wrong, it's because you have to factor in that one of the lobes of the figure 8 is reverse phase.

Sometimes they do make cardioid mics exactly like that, with two diaphragms, but mostly they use an acoustic phase delay network on one side to create the cardioid shape, which is even more ninja. For all the info there is about mics on the web, there's very little on how they really work - which made this Neumann PDF I came across recently a real find. /mics derail

posted by iotic at 11:20 AM on August 31, 2012 [4 favorites]

Sometimes they do make cardioid mics exactly like that, with two diaphragms, but mostly they use an acoustic phase delay network on one side to create the cardioid shape, which is even more ninja. For all the info there is about mics on the web, there's very little on how they really work - which made this Neumann PDF I came across recently a real find. /mics derail

posted by iotic at 11:20 AM on August 31, 2012 [4 favorites]

*/mics derail*

The cool part is that it's actually totally on-topic!

posted by odinsdream at 11:32 AM on August 31, 2012 [1 favorite]

Vi Hart is a national treasure. Her videos are mathematically correct spoken word poems.

posted by gwint at 11:34 AM on August 31, 2012 [4 favorites]

posted by gwint at 11:34 AM on August 31, 2012 [4 favorites]

I appreciate what Vi Hart is all about and everything, she gets into lots of interesting stuff in an accessible way, and is clearly intelligent and well informed, but god is she ever

posted by Nomiconic at 12:37 PM on August 31, 2012 [1 favorite]

*smarmy.*posted by Nomiconic at 12:37 PM on August 31, 2012 [1 favorite]

In high school, a math teacher drew something very much like this. He asked the class whether anyone knew what it was.

It looked like a cardioid with a hole in it, so I thought I would make a joke about a graph with a heart condition of some sort. I said "that's a cardioid with angina".

But this was high school; no one heard it as "

posted by Jpfed at 12:43 PM on August 31, 2012

It looked like a cardioid with a hole in it, so I thought I would make a joke about a graph with a heart condition of some sort. I said "that's a cardioid with angina".

But this was high school; no one heard it as "

*gina". So the whole class erupted in laughter at a joke that I didn't make, but probably should've.***an**posted by Jpfed at 12:43 PM on August 31, 2012

*I wish she'd slow her speech down just a little.*

No. Please do not do this.

posted by Hollywood Upstairs Medical College at 1:22 PM on August 31, 2012 [2 favorites]

I love watching her videos. She's a smart girl, not only for her mathematically tuned brain, but for a lot of the insight she sneaks inbetween those dots:

posted by FirstMateKate at 1:28 PM on August 31, 2012 [3 favorites]

*"..and you don't want to learn to graph them, even if it means not making a billion dollars from a game about shooting birds at things. Meanwhile, anyone learning*

But teaching**how**to think mathematically can then learn to graph a parabola or anything else they need in like five minutes.But teaching

**how**to think is an individualized process that gives power and responsibility to individuals, while teaching**what**to think can be don with one-size-fits-all bullet points and check boxes. And our culture of excuses demands that we do the latter, keeping ourselves placated in the comforting structure of tautology and clear expectations."posted by FirstMateKate at 1:28 PM on August 31, 2012 [3 favorites]

Swell video! While we're here, a glance at a personal fave, the Famous Curves Index. Find a name for your art-rock band here. And yes, the straight line is really a curve, in its own way.

posted by ovvl at 1:50 PM on August 31, 2012 [1 favorite]

posted by ovvl at 1:50 PM on August 31, 2012 [1 favorite]

Aw darn it, she stopped just before inventing calculus.

Cardioids are just a type of cycloid, an epicycloid to be specific. Isaac Newton basically invented calculus while studying cardoids.

For a really good (but hardcore) explanation, I highly recommend watching The Birth of Calculus by Jeremy Gray. He travels to various European libraries to find Newton's original notebooks, and reads from them while explaining the history of how Newton invented calculus. The interesting bit about cycloids is about here, with some good animations of cycloids and the calculating tangents of the cycloid, which gets you calculus.

That whole video by Vi Hart was about tangents, and she never used the word once.

posted by charlie don't surf at 4:42 PM on August 31, 2012 [1 favorite]

Cardioids are just a type of cycloid, an epicycloid to be specific. Isaac Newton basically invented calculus while studying cardoids.

For a really good (but hardcore) explanation, I highly recommend watching The Birth of Calculus by Jeremy Gray. He travels to various European libraries to find Newton's original notebooks, and reads from them while explaining the history of how Newton invented calculus. The interesting bit about cycloids is about here, with some good animations of cycloids and the calculating tangents of the cycloid, which gets you calculus.

That whole video by Vi Hart was about tangents, and she never used the word once.

posted by charlie don't surf at 4:42 PM on August 31, 2012 [1 favorite]

*Meanwhile, anyone learning how to think mathematically can then learn to graph a parabola or anything else they need in like five minutes.*

I have to teach my classes how to graph parabolas. When I started out, I thought I could instead teach them to think mathematically (and god knows I still try) but, they both can't and don't want to learn that.

posted by Obscure Reference at 5:02 PM on August 31, 2012 [3 favorites]

*I have to teach my classes how to graph parabolas. When I started out, I thought I could instead teach them to think mathematically (and god knows I still try) but, they both can't and don't want to learn that.*

I'm currently working at a job grading standardized math tests. Yes, kids can and do learn to think mathematically. They can graph parabolas and some of them can even come up with surprising ideas and methods that cause intense debate within our panel of experts with advanced degrees in math.

So I think that video is a bit patronizing to students. Raise your expectations of students, and some will rise to the challenge.

posted by charlie don't surf at 5:30 PM on August 31, 2012

I had an absolutely fabulous calculus teacher who somehow managed [through sorcery, most likely] to simultaneously teach both how and what to think. I can sort of think mathematically, especially when there's some physical aspect to it, like those graph of cycloids, or calculus when it relates to physics, or just calculus in general. I'm pretty envious of people who can think more abstractly about math, but then there are people I know who are jealous of my spatial relation skills. Give and take, I guess.

posted by FirstMateKate at 5:35 PM on August 31, 2012

posted by FirstMateKate at 5:35 PM on August 31, 2012

My 13 year old is pretty annoyed that Algebra I (in 8th grade) isn't teaching him analytic geometry or even the quadratic formula. But he was pretty psyched when I gave him a problem in base -10. (If you like that, try base 2i. My officemate and I spent pretty much the whole "work"ing day on those.)

All the kids love Vi Hart. She's the best.

posted by DU at 5:50 PM on August 31, 2012

All the kids love Vi Hart. She's the best.

posted by DU at 5:50 PM on August 31, 2012

God I wish someone had taught maths like this when I was in high school.

posted by smoke at 6:57 PM on August 31, 2012

posted by smoke at 6:57 PM on August 31, 2012

*When I started out, I thought I could instead teach them to think mathematically (and god knows I still try) but, they both can't and don't want to learn that.*

There was nothing more frustrating as a math tutor than hearing "just give me the formula". Learn how limits work, and then you will know all the formulas for the rest of the class...

posted by Jpfed at 10:28 PM on August 31, 2012 [1 favorite]

My friend made a video inspired by this! He likes doodling with Mathematica instead of pencils, so you get some computer-generated animations of lines and curves - here's a link (semi-self-link since I help edit his blog). I can probably convince him to explain his methods if somebody else wants to play around with this too.

posted by dreamyshade at 4:27 AM on September 1, 2012 [1 favorite]

posted by dreamyshade at 4:27 AM on September 1, 2012 [1 favorite]

The excitement continues! Part 2 of Rolling Circles and Balls is now up!

posted by odinsdream at 6:23 AM on September 3, 2012

posted by odinsdream at 6:23 AM on September 3, 2012

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posted by bonehead at 10:40 AM on August 31, 2012