[PenultimateManStanding]

This comes from Hippocrates of Chios (not the doctor one) who studied lunes (moon-shaped figures created by intersection of circles) I'll describe this with modern terms: consider the unit circle and plot the points created by the intersection of rotating a ray of length one counterclockwise 90 degrees (pi/2 radians) while moving a vertical line backwards from one to zero on the x-axis. for example, if the ray is rotated 1/4 of the way to 90 degrees, the vertical line has moved 1/4 of the way from 1 to 0 (and lies at x=3/4). So plotting all of these points creates a curve beneath the quarter circle created by the ray rotating. Heres the amazing thing if you can follow the description so far: when the ray has rotated 90 degrees so the ray points up along the y-axis, the other curve crosses the y axis at 2/pi: the inverse of the radian rotation of the ray (pi/2). This point can be used to square the circle (but there's a catch in that the point is a limit)


It looks very interesting if you plot some of these points and sketch the lower curve. You can see that it crosses the y-axis at around 2/3. I calculated it using the expression for the points of intersection being: x tan[(1-x)90]
if you set x very small you get approximately 2/pi. clearly if x=0 the expression doesn't work, which is related to the fact that the circle can't actually be squared.

[NEOPO]

[PenultimateManStanding]

the area of the lune is equal to the area of the inscribed triangle. It's not hard to see why using the pythagorean theorem and looking at the areas of the squares on the similar chords which happen to be the sides of the inscribed right isosceles triange. Hippocrates was the first to find the quadrature of a circular shape in this way.

[cynicalheretic]

Dude, seriously, go smoke some damn weed.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('cynicalheretic', 'D')ude, seriously, go smoke some damn weed.

[gampy]

Ahhh...the joy of discovering mathematics and geometry. I remember playing with rulers and those circumscribing thingies in English class when I should have been paying attention to Shakepeare's sonnets.

To think that these fellows in antiquity discovered all this stuff for the first time! To have that "Eureka!" moment.

It is so profound to see God in a circle, square and triangle.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('gampy', ' ')
It is so profound to see God in a circle, square and triangle.

[cynicalheretic]

$this->bbcode_second_pass_quote('PenultimateManStanding', '')$this->bbcode_second_pass_quote('gampy', ' ')
It is so profound to see God in a circle, square and triangle.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('cynicalheretic', '[')
It's amazing PMS, only you could be a big enough geek to nerd up a forum about hydrocarbon depletion

[MD]

This is where I admit to a thrill of euphoria that lasted for three days after I learned how to calculate pi through calculus...

yup...it's true...that kind of shit reaches deep in my soul.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('MD', 'T')his is where I admit to a thrill of euphoria that lasted for three days after I learned how to calculate pi through calculus...

yup...it's true...that kind of shit reaches deep in my soul.

[PenultimateManStanding]

Archimedes was working out one of his brilliant ideas, and they were brilliant, he was the best mathematician of the ancient age, when the Romans overran Syraceus. Some ignorant soldier killed him because Archimedes was too rapt in attention to the language of the Universe.

[gampy]

I am trying to remember my first mathematical epiphany.
Sorry for the religious references, but I suppose there is something of the religious in the pursuit and capture of knowledge, and understanding.

Hahaha...I remember. I was in 3rd grade I think. Our class was beginning to study fractions and the addition and subtraction thereof.
I could not grasp the concept until my family was having pizza for supper, and my mother asked how much was left, so I had to add up the slices from 3 different boxes. I still remember using that visualization when doing the quizzes. All the fractions were pizza slices, and the whole numbers were pizzas. It worked!

And getting my head around the idea of multiplying negative integers.
That was satisfying, once I fully understood.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('gampy', 'I') am trying to remember my first mathematical epiphany.
Sorry for the religious references, but I suppose there is something of the religious in the pursuit and capture of knowledge, and understanding.

Hahaha...I remember. I was in 3rd grade I think. Our class was beginning to study fractions and the addition and subtraction thereof.
I could not grasp the concept until my family was having pizza for supper, and my mother asked how much was left, so I had to add up the slices from 3 different boxes. I still remember using that visualization when doing the quizzes. All the fractions were pizza slices, and the whole numbers were pizzas. It worked!

And getting my head around the idea of multiplying negative integers.
That was satisfying, once I fully understood.

[gampy]

$this->bbcode_second_pass_quote('PenultimateManStanding', '')$this->bbcode_second_pass_quote('gampy', 'I') am trying to remember my first mathematical epiphany.
Sorry for the religious references, but I suppose there is something of the religious in the pursuit and capture of knowledge, and understanding.

Hahaha...I remember. I was in 3rd grade I think. Our class was beginning to study fractions and the addition and subtraction thereof.
I could not grasp the concept until my family was having pizza for supper, and my mother asked how much was left, so I had to add up the slices from 3 different boxes. I still remember using that visualization when doing the quizzes. All the fractions were pizza slices, and the whole numbers were pizzas. It worked!

And getting my head around the idea of multiplying negative integers.
That was satisfying, once I fully understood.

[cynicalheretic]

You broke the 8000 post barrier... congratulations are in order I guess. Or pity is due, I am not sure which

[PenultimateManStanding]

I recall that studies show only 5% of people are able to understand what is expected that teachers are supposed to show all young students for comprehension about mathematics. It's absurd. This is why I chose to be a sub. I won't be captured by an existential absurdity.

[cynicalheretic]

In highschool I understand everything my teachers talked about. College on the other hand, what the fuck am I doing studying about petrology from a guy who believes that Oil is abiotic.

[peaker_2005]

$this->bbcode_second_pass_quote('cynicalheretic', 'I')n highschool I understand everything my teachers talked about. College on the other hand, what the fuck am I doing studying about petrology from a guy who believes that Oil is abiotic.

[MD]

An early mathematical epiphany of mine occured when I was bouncing a ball and realized that "hey, if it rebounds to a fraction of it's height each time, then it should bounce forever". I then spent quite a while counting bounces. The "superballs" were the best. The original black ones that came in various sizes were my favorites.

To this day I'd like to try it in a vacuum with various materials. I bet you could get bounce counts in the thousands. The tail-off curves would be immensely interesting, I'm sure.

Surely some school science class has done this . . . time for a quick google.