A line that intersects only one point on a circle so that a perpendicular line could be made off that point is not possible, because the line would hit an infinite number of points on the circle before reaching just one point on the edge of the circle. Sure you can specify one point on a circle, but the line is touching infinitely more than just one point as well as that single point. Touch one point on a triangle, sure. Circle, no.
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Anonymous2006-04-03 16:16
Define a circle by the identity
x^2 + y^2 = a^2
then for any tangent of the circle, there is only one pair (x,y) contained in the tangent AND the circle.
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Anonymous2006-04-03 17:06
>>1
Take a calculus course. If you think you can draw a tangent on a triangle, which is made of three straight line segments, then a circle, being made from an infinite amount of infinitely small straight lines, can have a line drawn tangent to it.
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Anonymous2006-04-05 2:58
>>1
.... This is not win. Back to grade school with you.
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Anonymous2006-04-06 12:15
Depends how large the point in question is meant to be. Is a point classified as a single atom, or a set of millions of atoms? A point could be an inch or a foot or a yard or a mile.
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Anonymous2006-04-06 15:11
>>how large the point
think about what's wrong with that.
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Anonymous2006-04-06 15:46 (sage)
A point is a zero-dimensional object, amirite?
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Anonymous2006-04-06 16:03
>>7
Technically it's not as an existant object can not be "0D".
>>10
It wouldn't exist in a tangible dimension (i.e length, width, depth, time), and thus it would be non-existant.
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Anonymous2006-04-07 3:53
>>7,8,10,11
A point is "dimensionless without any properties except location" according to Dictionary.com. Although it is dimensionless, it cannot be '0D' because, as >>11 said, it would not able to exist.
This brings me back to the POINT (haha) I was trying to make in >>5: A 'point' in mathmatics is as large or small as the viewer percieves it, because a point is undefined and CANNOT be defined until we revise math as we know it.
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Anonymous2006-04-07 9:21
Uhm, but if it is 'dimensionless', it wouldn't exist in a tangible dimension either, no?
Seeing the point, line, plane, etc progression as objects of increasingly higher dimension, starting with zero, makes perfect mathematical sense, AFAICS.
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Anonymous2006-04-07 10:24
>>12
a point in mathematics is infinitely small, since if it were finitely small, it would have a finite size, and thus would be a line, if not a higher dimensional figure.
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Anonymous2006-04-07 11:00 (sage)
Mathworld says a point is 0-dimensional, that's good enough for me.
>>15
That guy's an asshole though. Besides they've been wrong before, for instance their quaternion rotation formulas were wrong.
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Anonymous2006-04-07 12:21
sure a point doesn't exist in reality, it's just a useful mathematical construct, and used to model some real life situations. all I was trying to point out, is that its incorrect to talk about the size of a point, because it's just a point.
so we don't need to revise maths as we know it, we just need to be careful about the terms we use.
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Anonymous2006-04-08 2:36
The general progression is point, line, plane, solid for 0-d, 1-d, 2-d, 3-d. Read "Flatland" sometime, it really helps drive this stuff home. Technically, however, in most mathematics, "point" is either (1) undefined, in geometry classes (Euclid defined it as "that which has no part", which is completely meaningless) or (2) an ordered n-tuple, in algebra classes when working in an n-dimensional space.