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Pi is wrong

This is a discussion on Pi is wrong within the General Off Topic+ forums, part of the QJ.net Forum Miscellaneous category; http://www.math.utah.edu/~palais/pi.html I know why the above article is incorrect. A cookie to whomever finds out :]. Hint: Something is wrong ...

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1. Pi is wrong

http://www.math.utah.edu/~palais/pi.html

I know why the above article is incorrect. A cookie to whomever finds out :].

Hint: Something is wrong with what he used to prove his point.

2. me no good at math

3. Pi's correct, leave it at that.

4. he's using radius, thats why its 2(pi) instead of just pi. Pi is the ratio between diameter and circumference

5. Is it something to do when he's talking about the circle in 4ths?

6. because a circle has infinate sides pi can never be exact pi is just as close as weve been able to get to the correct ratio.

7. Originally Posted by Realn0whereman
because a circle has infinate sides pi can never be exact pi is just as close as weve been able to get to the correct ratio.
And that's why Bob looks stupid.

8. pi is 3.14...

and

circle doesn't have infinite side!!

9. Originally Posted by lianne777
circle doesn't have infinite side!!
How many does it have?

10. Circle doesn't have sides.
-= Double Post =-
if it has side it will be called Polygon.
-= Double Post =-
if it has side it would have been called "Polygon"

11. circles have NO sides here is why:

a circle is defined to have ALL points equidistant to the center. if a circle had a side, any point on that side (except the end point) would not be equidistant to the side.

12. a circle has one side

13. depends on how you define a side

14. isn't 1 side a straight edge? so if u have infinte straight edges connected to one another and the last one is connected to the first, won't u have a circle?

15. Originally Posted by gurpz1
isn't 1 side a straight edge? so if u have infinte straight edges connected to one another and the last one is connected to the first, won't u have a circle?
no because the midpoints of those edges wont be equidistant to the center, no matter how infinitely small they get.

16. if the lines are all the same length and at the same angle they will, wont they??

17. The article isn't incorrect. He's just saying that it would be more sensible to define the constant pi as 2pi, which it would.

18. Originally Posted by gurpz1
if the lines are all the same length and at the same angle they will, wont they??
no. since the midpoint of the line, must be the same distance from the center as the endpoints of the line in order for this to be circle, which is impossible since the vertex bisector of an isosceles triangle cannot be the same lengths as the legs.

19. Pi is the number obtained when the diameter of the cricle is divided by the circumference. The guy who wrote that is an idiot, at least I hope he is because I have a Maths IGCSE tomorrow!

20. Originally Posted by captainX
Pi is the number obtained when the diameter of the cricle is divided by the circumference. The guy who wrote that is an idiot, at least I hope he is because I have a Maths IGCSE tomorrow!
You do realise that the angles of a circle can be represented by pi aswell, right?

21. Originally Posted by lianne777
Circle doesn't have sides.
-= Double Post =-
if it has side it will be called Polygon.
-= Double Post =-
if it has side it would have been called "Polygon"
Well, you could define a circle in terms of polygons and limits.

A circle is a standard polygon with n sides as n.

22. no!!

side is formed by an angle.
does the circle have angles?NO!

the side of a circle is called "circumference" so stop calling the Circumference the side of a circle.

23. Originally Posted by lianne777
no!!

side is formed by an angle.
does the circle have angles?NO!

the side of a circle is called "circumference" so stop calling the Circumference the side of a circle.
Does your brain implode when you see a sphere then?

24. Originally Posted by msten19
Well, you could define a circle in terms of polygons and limits.

A circle is a standard polygon with n sides as n.
cant you read, if you failed to read before, maybe this will help:
no. since the midpoint of the line, must be the same distance from the center as the endpoints of the line in order for this to be circle, which is impossible since the vertex bisector of an isosceles triangle cannot be the same lengths as the legs.
it doesnt matter how infinitely small the sides get, because, no matter what, you will always have this problem.

25. Jesus Christ, are you people honestly arguing over how many sides a circle has? Contrary to popular belief, the real world is not made up of polygons. A perfect circle (impossible, but hypothetical), has NO sides. If it had ∞ sides, then the angle between each side would have to be 0. since 0 * ∞ = 0, that would make your circle a straight line... 'Infinigons' DO NOT EXIST!

A circle is a shape where all points are the same exact distance from a central point. is as simple as that. True polygons only exist in computer generated graphics, reality isn't computer generated...

This whole thing is similar to the arguement that (10/3)*3 = 9.999999(infinitely repeating)...

10/3 - 3.333333(infinitely repeating)
So, logically, 3.333333(infinitely repeating)*3 should be 9.999999(infinitely repeating), right?

Wrong! Since you have both division and multiplication by the same integer, the equasion can be simplified to 10 = 10. Also, if you use (10/2)*2, you have no infinately repeating decimals, so it just equals 10.

Math is very simple, don't try to make it complicated by throwing ∞ into the mix. ∞ is NOT a number, it has no value. If anyone can tell me the value of ∞ (In standard notation), please do...

26. actually the measure of the interior angle wouldn't be zero since the way you determine the measure of a interior angle is
(n-2)(180)/n

(∞-2)(180)/∞ does not equal zero

27. Arguments about the number of sides of a circle aside, what the did thread starter find wrong with the article? I can't see anything incorrect about it and personally I agree with the author.

28. Originally Posted by lianne777
no!!

side is formed by an angle.
does the circle have angles?NO!

the side of a circle is called "circumference" so stop calling the Circumference the side of a circle.
A circle is a one-sided plane figure. The number of sides in a closed plane figure is equal to the number of angles. and a circle has a 360-degree angle.

brainleak engaged

Originally Posted by captainX
Pi is the number obtained when the diameter of the cricle is divided by the circumference. The guy who wrote that is an idiot, at least I hope he is because I have a Maths IGCSE tomorrow!
He's not an idiot. He makes perfect sense.

29. Originally Posted by dracule
actually the measure of the interior angle wouldn't be zero since the way you determine the measure of a interior angle is
(n-2)(180)/n

(∞-2)(180)/∞ does not equal zero
ok, first of all ∞-2 = ∞, so it ∞ cannot even be an number since it doesn't change when added, subtracted, muliplied, divided, etc.

So, logically, treating ∞ as a theortically veriable:
(∞-2)(180)/∞
(∞)(180)/∞
∞/∞
1

Do you see the problem in this?

Honestly, think about what you are arguing here. You are arguing how many sides a circle has... This is just dumb... There is a difference between geometry and trigonometry; ever wonder why graphing calculators have Degree/Radian/Gradian modes?

And to get back on the original topic:

I feel that A=πr² is a lot easier than A=(πr²)/2. Thats why π≠2π. then people try to use C=2πr as a reason why π should equal 2π. But if you used diameter instead of radius, you would have C=πd.

Pi is fine the way it is, diameter and radius are directly proportional, so I don't see what the problem is.

30. How many sides does a circle have?
There are two sources of ambiguity here.

1. The word CIRCLE sometimes refers to a circular disk (because it is common to talk about "the area of a circle"), but often the word refers only to the boundary of the disk (namely, the points that are equally distant from the point at the center of the figure).

2. The meaning of the word SIDE depends on its context. A polygon in the plane has, by definition, n vertices and each pair of consecutive vertices are joined by a side. It is clear that a polygon with n vertices has n sides. In general, the word side depends on the dimension of the figure -- a side is always part of the boundary.

So what is the side of a circle? If you think of the circle as a disk then it it has an up-side and a down-side. If you think of it as a curve, then it has an inside and an outside. If you think of it as the limit of an n-sided regular polygon, then one can justify the answer that the circle has infinitely many infinitesimal sides. Our conclusion:
the question, "How many sides does a circle have?", is too ambiguous to have a definite answer.
Perhaps the appropriate response is "there is no natural way of saying what the side of a circle is."
My opinion (and the opinion of my geometry teacher) is that a plane figure's 'side' is a continuous segment of its boundary, so a circle has one side. The point is that it doesn't freaking matter.

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