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## Mathematics is a tool.

Mathematics is a tool.

"The United States can pay any debt it has because we can always print money to do that." — Alan Greenspan## Is that an insult?

.

## So...

I can envision Archimedes or someone of his time...

Imagining a unit of counting. And measuring a circle's radius with merely a straight edge and a compass (which she may superficially mention) as being one unit of counting.

And making a unit circle out of that.

Of course. You COULD cut everything in half.

But then you only get half the knowledge lol

## Actually...

I would suggest to this girl to study Euclid better. As well as Archimedes, Thales, Pythagoras, Descartes, all the greats...

She's trying to make a simple conversion to appeal to one's 'common sense' of seeing the circumference as a PIE or a piece of food?

LOL when, if you actually look at the material and try to do calculations, its easier to understand what has been formulated already and what is actually true.

Essentially she just cuts everything in half and in the end DOES abolish or change Euclid's equation (like she claimed she 'wouldnt') by making it π/2 = θ instead of π.

## Did you watch any of her other videos?

I like it because my nine year old daughter is in love. She doesn't even understand the half of it, but she watches the videos often enough to develop an interest in math.

I am quite satisfied. To be honest I would be kinda worried if this was satisfactory to a duel math/physics major.

Séamusín

## Oh

I have only seen the pi and the net neutrality one. I loved the net neutrality one, but I thought the pi video was a bit - dare I say - "common core" in that it dumbed down the original understanding of the concept. At least MY original understanding which was based on Archimedes and Euclids work on geometry.

I am intrigued enough to have to look at her videos now. I love her style though, with the drawings and writings carrying you along.

## Well it was

It was interesting and was enough to spark an objective and critical view from me! =)

Like I said, her method and understanding WAS technically correct. But I learned the unit circle.

It wasn't until later that I studied Archimedes and Euclid a bit and understood why the unit circle was the way it was. But it makes sense to me.

That's awesome though that she's nine and getting interested in stuff like this, dude... I was nine once and I think I recall my main interests as Pokemon and riding my bike... But certainly I wasn't into anything as thought-provoking as that.

Yeah I'm a Junior and I've always had a really good knack for math and numbers, plus I've always appreciated science (dont we all?)... So physics seemed about right. It was always tough for me (dont we all struggle?), but I wanted to strive for it so here I am lol...

## watched the whole video...

didn't understand one fucking thing...

## Probably

Cause she's essentially trying to improve an Archimedes' and Eulers' method/work by making a simple conversion - which for some reason she superficially laments a conversion, but then goes ahead and uses one in a more confusing (and less intuitive) manner.

I think her attempt is to explain to the lay-person why it's "better" or "easier" for one to use π radians instead 2π radians for the measurement of circumference.

Essentially, her conversion simply applies a factor of 1/2.

However, if you were to study Descartes and Pythagoreas and the unit circle, and how Archimedes derived π... As well as the various calculations used in applied trigonometry (which essentially revolves around angles and the unit circle)... It's much more intuitive and sensible (and easier) to use 2π for the radian measurement of a circumference when it comes to calculations.

Like I said, her method is correct, but I don't understand why she's trying to improve on Archimedes and Euler and the great mathematicians throughout history, and the beautifully elegant, commonsense, and accepted methodologies they derived and which have been used for millennia.

In my opinion and from my perspective, she means to make things more understandable but is just making things more confusing...

If you'd like to understand more, I'd suggest you study the unit circle, sin/cos/tan, Archimedes and the geometry of a circle, Cartesian coordinates, Euclidean geometry, etc.

## ooooohhh that's why i don't

ooooohhh that's why i don't understand it. i thought it was because im a high school drop out that failed algebra 1A. silly me hahaha :)

## lol...

Touche.

But hey man, algebra can be quite tough and is quite an extensive field. Linear algebra is one of the most complex subjects in mathematics.

And I've found from my studies and asking my math and physics professors that most of the mistakes made when doing calculus (or most any other) calculations are algebra mistakes.

## 2pi = 0 & -pi = pi on the

2pi = 0 & -pi = pi on the complex plane.

## Yes

And she says "the way of mathematics is to MAKE STUFF UP until it makes sense"?!

I'd rather say it's using a common terminology as well as axioms, measurements, observations, and Cartesian common sense to understand and define problems and ideas which are already present.

LOL... Nowhere in the video does she try to hit home the point that π is the relation of diameter (not radius) and circumference. And she doesn't mention Archimedes and his method of deriving π - she's wrong when she says the radius and not the diameter is the fundamental idea you use in determining the circumference.

http://www.pbs.org/wgbh/nova/physics/approximating-pi.html

Well, technically she's not wrong, but she's making a observation which is stating the same thing as what Archimedes said, just making it less simple. She's just using a simple conversion to justify her method. In fact, in the beginning she rants about the simple "conversion" (which technically isn't a conversion but the way it's been understood, derived, and done for thousands of years) - but then she goes on to use tau as HER conversion.

AND like you said (essentially), if you're dealing with a plane centered at zero, with radius 1 (from -1 to 1), your value of the circumference would be 2π.

And when calculating sinθ, cosθ, and tanθ on a unit circle... You want the radius to be 1 and the circumference to be 2π for simplicity because sinθ = y/r, cosθ = x/r, and tanθ = y/x.

When a circle's radius is 1, its circumference is 2π. When a circle's diameter is 1, its circumference is π.

Which is also why it's common practice to define 2π as the circumference in radians - it's completely commonsense and more mathematically simple than her method.

I'm sorry... As a dual math and physics major and someone who has always got a great deal of sense out of mathematics... This video and her methodology - which was ultimately correct - was just a conversion which tends to complicate things (at least from my viewpoint) when dealing with calculations.

## Love all her videos

Wish she was my teacher growing up