Question

π=4 ?!

Answer 1

Pi isn't 4?
It's 3.14. . .

Answer 2

Ofcourse I know that ...But find whats the mistake with this proof ^^

Answer 3

Haha, I'll try XD

Answer 4

@Callisto :) pie

Answer 5

the mistake is that you can't do it again without intruding inside the circle

Answer 6

if you repeat that operation to infinity, you'll still have corners to remove, right?
a circle has no corners.

Answer 7

@euler I dont think so

Answer 8

the circle is only touched tangentially four times (as defined at the start). To find the circumference you must touch it tangentially in all places. At no time will the function's rectilinear surface length resolve to a valid approximation of the circle for this reason (among others)

Answer 9

Bhen limit tends to infinity there is a possibility all the ends become tangential to the circle

Answer 10

*But when

Answer 11

Yea true ,But difference between the euclidean metric and the "taxicab metric". The euclidean length of a segment : \[\Delta Z=(\Delta X,\Delta Y)~is ~\sqrt{\Delta X^2+\Delta Y^2}\] whereas the "taxicab" length of this segment is \[|\Delta X | +|\Delta Y |\]. "In the limit" this implies that the euclidean circumference of the unit circle is \[2\Pi\], whereas the "taxicab circumference" is 4.

Answer 12

lol I dont have any idea of those

Answer 13

The reason I have with me is :

These are *pointwise* convergent, but not *uniformly* convergent, and hence the path length of the limit isn't necessarily the limit of the sequence of path lengths.

Answer 14

Its about Euclidean distance and taxicab distance.

Answer 15

Good :)

Answer 16

Yea ,your point of view is right ..
Anyway , If you do π approximation by using the area of the figures that the approximation does approach the actual value of π.... You can then tell them that while the area of the figure is approaching the area of the circle the perimeter doesn't approach the circumference, because of the way that it was cut.

Answer 17

so could you approximate pi like this using area?

Answer 18

Thanks for providing different solutions @Eyad

Answer 19

@Peter14 :Yes ,But it shouldn't be approach the actual value of pi to provide a certain part of it .
@AravindG :Nice Idea ! :)

Answer 20

:) next question is up !