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/sci/ - Science & Math

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7975463 No.7975463 [Reply] [Original]

What precisely is an angle? The problem is that defining an angle correctly requires calculus. This is a point implicit in Archimedes' derivation of the length of the circumference of a circle, using an infinite sequence of successively refined approximations with regular polygons. It is also supported by the fact that The Elements [Euclid] does not try to measure angles, with the exception of right angles and some related special cases. Further evidence can be found in the universal reluctance of traditional texts to spell out a clear definition of this supposedly "basic" concept.

>> No.7975468

>>7975463
an angle is the degree of parallelity between two lines

180 degrees is negative parallel

0 degrees is positive paralell

90 degrees is positive non paralel

270 degrees is negative non parallell

kinda simple definition desu, dont overthink it

>> No.7975476

>>7975468

How does one measure this "parallelity"?

>> No.7975480

>>7975476
by taking the angle of two lines

>> No.7975482
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7975482

Did somebody say 'intelligible plane geometry'?

>> No.7975484

>>7975480

Too vague.

>> No.7975489
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7975489

>>7975463
and angle is the number A so that
R.A = length of the arc on the circle of radius R, with angle A

OP is not a bright HS student....

>> No.7975495

I'm pretty confident you could define an angle rigourously using two position vectors and an origin

>> No.7975496

>>7975463
>The problem is that defining an angle correctly requires calculus
No, it doesn't.

>> No.7975500

>>7975489
>angles can only be defined with circles

>> No.7975511

>>7975468
best answer

>> No.7975550

>>7975489

Define arc.

>> No.7975577

>>7975550
an angled line

>> No.7975600

>>7975500
>only
who said that ?

>> No.7975603

>>7975600
Did you forget what greentext is?

>> No.7975613

>>7975463
It's how bent something is. For instance, a RIGHT angle is the angle that your mom is at when I fuck her RIGHT in the ass.

I don't think there's an argument in the world that will convince me that any angle that can't be made with a compass and a straight-edge doesn't exist.

>> No.7975644

>>7975550
https://en.wikipedia.org/wiki/Arc_length#Generalization_to_.28pseudo-.29Riemannian_manifolds

>> No.7976037

>>7975644
>>7975613
>>7975577

Not good enough /sci/.

>> No.7976042
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7976042

>>7975463
Dumb gorilla poster

>> No.7976052

>>7976042

Dumb - that one guy, ever, who does this - bear poster.

>> No.7976100
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7976100

>>7976052
>he thinks there's only one bear poster

>> No.7976140

Depends.
In geometry, it's defined using three points.
In linear algebra, it's defined using scalar product.

>> No.7976153

An angle is an orbit of couples of unit vectors under the action of the group of rotations of your space.

>> No.7976160

>>7975463
The figure formed by two rays which share a common end-point, or vertex.

>> No.7976175
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7976175

>>7975489
Pretty rad, bro

>> No.7976250

>>7975463
Kim is best waifu.