February 10, 2012 12:10 PM Subscribe

There were ways to find the tangent to a curve, and the area under one, in an ad hoc manner before the birth of calculus. It was even known that these two were inverses of each other.

posted by Obscure Reference (17 comments total) 30 users marked this as a favorite

posted by Obscure Reference (17 comments total) 30 users marked this as a favorite

I can't believe how roughly he's handling those books!

posted by mrnutty at 12:22 PM on February 10, 2012 [4 favorites]

posted by mrnutty at 12:22 PM on February 10, 2012 [4 favorites]

Huh. That tangential circle is called the Osculating Circle, which means 'kissing.' As I recall, it actually agrees in its second derivative, as well, at the point of osculation.

Cool find! I'll probably pass this along to my students...

posted by kaibutsu at 12:36 PM on February 10, 2012

Cool find! I'll probably pass this along to my students...

posted by kaibutsu at 12:36 PM on February 10, 2012

I'm of the opinion that basic Physics, at least the force/acceleration/velocity/displacement relationship, needs to be taught before calculus. See, I played around with this stuff starting in 6th grade math classes using little sonic motion detectors and took a basic mechanics class before I started any calculus. Nobody actually explained that we were learning calculus at the time, but by the time I was being taught derivatives, I already had a really intuitive notion of how and why this stuff all worked.

Too many of my classmates saw calculus as complicated algebraic manipulation instead of the inevitable need to describe the relationship between the basic parameters of motion. Anybody who has taken Algebra 1 and has ever ridden in a car or pushed a toy train down a track can understand the basic concepts behind calculus. There's really no excuse for these concepts to be shoved into an "advanced" math class for selected students during their senior year of high school.

posted by zachlipton at 12:43 PM on February 10, 2012 [17 favorites]

Too many of my classmates saw calculus as complicated algebraic manipulation instead of the inevitable need to describe the relationship between the basic parameters of motion. Anybody who has taken Algebra 1 and has ever ridden in a car or pushed a toy train down a track can understand the basic concepts behind calculus. There's really no excuse for these concepts to be shoved into an "advanced" math class for selected students during their senior year of high school.

posted by zachlipton at 12:43 PM on February 10, 2012 [17 favorites]

they have to be facsimiles, mrnutty, they have to! I know people who would stop talking to me if I handled their comic books like that.

posted by valdesm at 12:45 PM on February 10, 2012 [1 favorite]

posted by valdesm at 12:45 PM on February 10, 2012 [1 favorite]

I'm of the opinion that basic Physics, at least the force/acceleration/velocity/displacement relationship, needs to be taught before calculusI'd say not the complete physics, but a simple investigation into mechanics would be the best. There is a tendency to get lost in the weeds in physics too. :-)

One issue I had when I was learning both was that I got the relationship between derivatives and physical motion, but did not really understand the integral in any intuitive way other than the geometric bar plot geometrical explanation.

From tht it was it was very unclear for the longest time how the tangent and area under the curve were even related... the idea that the anti-derivative "just worked" was something I could absorb as a fact, but didn't really make sense to me until later.

posted by smidgen at 1:00 PM on February 10, 2012

I agree. Newton didn't just invent calculus out of thin air. He invented it

posted by empath at 1:07 PM on February 10, 2012 [1 favorite]

For many students, calculus is more like an afterbirth.

posted by telstar at 1:46 PM on February 10, 2012 [1 favorite]

That they make you eat raw.

posted by taff at 2:08 PM on February 10, 2012 [2 favorites]

posted by taff at 2:08 PM on February 10, 2012 [2 favorites]

zachlipton, I'm off to check your profile gender, and if it's F/innie/grrl, I'm going to propose.

...

Damn.

posted by IAmBroom at 2:20 PM on February 10, 2012 [1 favorite]

...

Damn.

posted by IAmBroom at 2:20 PM on February 10, 2012 [1 favorite]

I came at it from the other side, with an unhealthy love of geometry. Newton's approach has always felt awkward and post-hoc while Leibniz explains something more of a basic discovery to me: exploring the properties of curves and shapes I can draw on paper or visualize on my own. Maybe it's just because I had a spirograph before you had a sonic motion detector, or you are a kinesthetic learner while I am a visual learner.

Anyhow, I thought the really great part of the video happens at the end where the approaches of Newton and Leibniz are compared and contrasted.

posted by peeedro at 2:34 PM on February 10, 2012 [1 favorite]

Sorry, and I'm straight too, but flattered! You can be my MeFi wife though if you'd like.

All other proposals should probably come through MeMail in fairness to the other candidates. Serious candidates only, don't call us we'll call you, void where prohibited, an equal housing lender, etc...

posted by zachlipton at 4:55 PM on February 10, 2012 [1 favorite]

How come the British put "the" in front of calculus but not in front of hospital?

posted by Grumpy old geek at 5:16 PM on February 10, 2012 [1 favorite]

posted by Grumpy old geek at 5:16 PM on February 10, 2012 [1 favorite]

I have spent 4 consecutive days on a temp job grading hundreds of high school algebra exams, while sitting next to a fellow whose presence compelled me to search in the company handbook to locate the policy statement, "Employees may be sent home if poor hygiene results in body odor." Now I'm at home on a friday evening watching a documentary on calculus. FML

posted by charlie don't surf at 6:25 PM on February 10, 2012 [1 favorite]

posted by charlie don't surf at 6:25 PM on February 10, 2012 [1 favorite]

Metafilter: reliable in practice, but it could be complicated to apply.

posted by ztdavis at 9:24 PM on February 10, 2012

posted by ztdavis at 9:24 PM on February 10, 2012

It makes calculus sound more important. Also, they have "maths" where Americans have "math" - like they have more than one math. Algebra is a math. Geometry is a math. And so on.

(Seriously, though, it's probably a shortening of "the differential calculus", as opposed to, say, the lambda calculus or the Schubert calculus. There's more than one calculus.)

posted by madcaptenor at 11:06 AM on February 11, 2012 [2 favorites]

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posted by Chocolate Pickle at 12:18 PM on February 10, 2012 [5 favorites]