Talk:One-dimensional space

Angle?

The last section says

The most popular coordinate systems are the number line and the angle.

In what sense can an angle be said to be a one-dimensional concept (bearing in mind that this article is entitled "One-dimensional space")? Loraof (talk) 22:42, 28 September 2017 (UTC)

I don’t see any problems with it: polar coordinates are a coordinate system, a two dimensional one with one coordinate being the radius the other the angle. Isolate either of those you have a one-dimensional system, so the angle can be considered a one-dimensional coordinate system in an obvious way. I edited it for better style but the mathematics is sound.--JohnBlackburne^words_deeds 23:08, 28 September 2017 (UTC)

• 
  Number line
• 
  Angle

Right now we have this image of the use of the angle to identify points. It has an x axis and a y axis, which implies 2-dimensionality. So at a minimum I think we should get rid of this image and replace it with something else. This image, unlike the one for the number line coordinate system, does not show the one-dimensional locus being traced out one-for-one with values of theta. So the replacement image ought to show a one-dimensional curve and three points: the point on the curve for which theta = 0, the angle's vertex (off the curve), and the point P (with the angle theta to P being shown).

I still dispute whether this can really be called a one-dimensional coordinate system, since the vertex is off of the one dimension, but at least this proposed diagram would be an improvement. Loraof (talk) 16:59, 29 September 2017 (UTC)

Circular angle is a parameter, not a space. In fact, it is a parameter of the exponential function as in Euler's formula. Another parameter of the same type is hyperbolic angle, also not a space even if in one-to-one correspondence with ℝ. The subject of how these two parameters complement one another was described in Introduction to the Analysis of the Infinite (1748); it is an important part of calculus. Suggesting that angle is a one-dimensional space is likely to spread confusion. — Rgdboer (talk) 21:48, 29 September 2017 (UTC)

I think you have misinterpreted my post. I am not suggesting that "angle is one-dimensional space". The angle is a parameter, and it identifies the location of a point in one-dimensional space, the topic of this article. The leftmost graph copied above shows the one-dimensional space in which locations are parametrized by x, but the rightmost graph unfortunately does not show the one-dimensional space in which locations are parametrized by theta. Instead, it shows two-dimensional space and three parameters: x, y, and theta, which doesn't make sense. Loraof (talk) 23:05, 29 September 2017 (UTC)

Angle is a one-dimensional coodinate, but the question here is can it be the coordinate of a one-dimensional space? "Angle" can only exist as a one-dimensional coordinate embedded in a two-dimensional (or higher) space. As the measure of the intersection of two lines, angles in 1-D space are all zero (or π). SpinningSpark 18:55, 18 August 2020 (UTC)

Hypersphere?

Surely it's Hyposphere. SpinningSpark 18:42, 18 August 2020 (UTC)