The answer is “it depends on how you defined the operation that acts on the circle”
What is the inverse of a circle?
11–20 of 51 posts
Re: What is the inverse of a circle?
#12The answer is “it depends on how you defined the operation that acts on the circle”
This is it. Inverse is a property of functions or other relational operators, not "static" individual objects. You need a direction in order to invert it.
Re: What is the inverse of a circle?
#13I did some wacky inside-out pics of planets years ago, inspired by the inside-out Mandelbrot set looking like a leaf/teardrop. https://www.adamponting.com/inside-out/ Related: Not Knot , 1991 Thurston-ish short film about knots and knot complements - "the space where the knot isn't". https://www.youtube.com/watch?v=zd_HGjH7QZo https://en.wikipedia.org/wiki/Not_Knot https://en.wikipedia.org/wiki/Knot_complement
That knot of Saturn looks like art to me. Anyway hats off for being to play with geometry like that.
Re: What is the inverse of a circle?
#14The answer is “it depends on how you defined the operation that acts on the circle”
As long as, C*Cinv = I, where C is the circle, Cinv is the inverse of circle, and I the identity. You're right. C, I, and * are entirely up in the air.
Re: What is the inverse of a circle?
#15A triangle?
Re: What is the inverse of a circle?
#16Mountain: inverse of a circle.
Molehill: reciprocal of all points in a circle on the complex plane.
Re: What is the inverse of a circle?
#17The answer is “it depends on how you defined the operation that acts on the circle”
This is it. Inverse is a property of functions or other relational operators, not "static" individual objects. You need a direction in order to invert it.
The multiplicative inverse, or reciprocal, or the inverse of a number, is a function acting on a number, 1/x, or x^-1.
Re: What is the inverse of a circle?
#18Earlier quoted context omitted.
This is it. Inverse is a property of functions or other relational operators, not "static" individual objects. You need a direction in order to invert it.
The multiplicative inverse, or reciprocal, or the inverse of a number, is a function acting on a number, 1/x, or x^-1.
Isn't this a case of multiplication being such a "well-known" function that the "inverse" defaults to "multiplicative inverse"?
Re: What is the inverse of a circle?
#19Earlier quoted context omitted.
This is it. Inverse is a property of functions or other relational operators, not "static" individual objects. You need a direction in order to invert it.
The multiplicative inverse, or reciprocal, or the inverse of a number, is a function acting on a number, 1/x, or x^-1.
The multiplicative inverse of a number n can be seen as the inverse of the function that multiplies its input by n. That is, the inverse of multiplication by n is multiplication by 1/n.
Similarly, the additive inverse of a number m is the inverse of the function that adds m to its input.
Re: What is the inverse of a circle?
#20I made this experiment I d3 quite some time ago.
http://bl.ocks.org/KKostya/6075142 http://bl.ocks.org/KKostya/6066548
Draw rectangle/circle on the right pane