Thales’ circles

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178 notes

curiosamathematica:

Pi in its full glory, popping up in all kinds of formulas.Which one do you find the most beautiful or intriguing?

I like its appearance in the values of various integral-defined functions: Gamma(1/2), the integral of exp(-x^2) over R (which is related to the error function), and the integral of sin(x)/x over R (which is the limit of the sine integral Si(x), and I didn’t know before today!). 

curiosamathematica:

Pi in its full glory, popping up in all kinds of formulas.
Which one do you find the most beautiful or intriguing?

I like its appearance in the values of various integral-defined functions: Gamma(1/2), the integral of exp(-x^2) over R (which is related to the error function), and the integral of sin(x)/x over R (which is the limit of the sine integral Si(x), and I didn’t know before today!). 

(via beautyandthemaths)

Filed under pi math integrals

1 note

A properly, conformally embedded once-punctured torus in R^3, parametrized by 

1/(1-sin(u)sin(v))*(cos(u)cos(v),cos(u)sin(v),sin(u)sin(v))

with 1≤u≤2π, 1≤v≤2π, obvs.

(A surface in R^3 is properly embedded if its intersection with any compact set is compact. Thus, the puncture in this surface is placed “at infinity”. A surface is conformally embedded if angles in the intrinsic metric match angles in the ambient metric. Here, you can see that latitude and longitude lines on the torus meet orthogonally.)

Filed under math torus

25 notes

twocubes:

How the heck does that work?

Well, first you think of one of these, but one dimensions up. Then, you conceive of a way to spin it around. Then, you intersect it with an appropriate hyperplane. Finally, you express this thought to a machine capable of generating an image from it. With your help, it should be able to produce something like this.

I would pay money to see slices of a 4d Menger sponge.

Filed under math Menger sponge 4d geometry

33,691 notes

(We’re taking a calculus final. The TA is a well-known Lord of the Rings fan, and we’ve had running LotR jokes all semester.)
TA:
“Okay, guys, everyone look at me. We’ve been over the rules, but just in case: no notes, pencil your answers in on the scantron sheet, and graphing calculators only – no more ‘can I just used my cell phone’ nonsense.”
Student:
“[TA's name], my calculator batteries just died! What should I do?”
TA:
“Here, I’ve got a big box of spares.”
Student:
*struggling* “I can’t get this packaging open…”
Student 2:
“Here, I’ve got a pocket knife.”
TA:
“And I’ve got a pair of scissors if you need them.”
Student 3:
*from the back of the room* “OR MY AXE!”
(Everyone starts laughing.)
TA:
“The only axes allowed on the exam are in the graph section.”
(Everyone groans.)
TA:
“Oh, come on, you’re in a math class. Deal with the math jokes.”
(The professor enters with a stack of exams. With him are two exam proctors.)
Professor:
“Tolkien jokes already, [TA's name]?”
TA:
“Hey, I didn’t start it.”
(The professor starts handing stacks of exams to the TA and proctors.)
Professor:
“But I’m about to finish it. [TA], take these exams down the left flank. [Proctor 1], follow the desks down the center. [Proctor 2], take your exams right, along the wall.”
(At this point, many of the students have realized where this is going:
Theoden’s lines from ‘Return of the King.’)
Professor:
“Forth, and fear no problems! Solve! Solve, students of calculus! Points shall be taken, scores shall be splintered! A pencil day! A red-ink day! Until three thirty!”
(The professor pulls out a pencil, holding it out like a sword, and runs down the first row holding it out. Students hold up their pencils, hitting his as he passes.)
Professor:
“Solve now! Solve now! Solve to good grades and the class ending! MAAATH!”
Entire Class:
“MAAATH!”
Professor:
“MAAAAATH!”
Entire Class:
“MAAAAAATH!”
Professor:
“Forth, exam-takers!”
(The entire class rises to their feet and gives him a standing ovation. A week later, we get an email from the professor.)
Professor:
*at the end of the email* “PS: I appreciate all of you who wrote in their evaluations that I was the one professor to rule them all, but the best one yet was the student who called me ‘Mathrandir.’”

Filed under math puns lord of the rings calculus final