circle inversion

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circle inversion englanniksi

1. (label) A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity.

2. 1875, A. B. Kempe, On Some New Limkages, Messenger of Mathematics, Volume 4, https://books.google.com.au/books?id=cpY_AQAAIAAJ&pg=PA121&dq=%22circle+inversion%22%7C%22circle+inversions%22&hl=en&sa=X&ved=0ahUKEwiDzsTgs9fNAhURNpQKHU-3BE0Q6AEIoQIwLgv=onepage&q=%22circle%20inversion%22%7C%22circle%20inversions%22&f=false page 121,

The first of these is obtained by the method of circle inversion first discovered by Peaucellier.

3. 1997, (w), MAA Notes, Issues 41-42, https://books.google.com.au/books?id=Ht3uAAAAMAAJ&q=%22circle+inversion%22%7C%22circle+inversions%22&dq=%22circle+inversion%22%7C%22circle+inversions%22&hl=en&sa=X&ved=0ahUKEwiDzsTgs9fNAhURNpQKHU-3BE0Q6AEIlAEwFA page 169,

Nikolai Joukowski (1847-1921) was a Russian mathematician who did research in aerodynamics (James and James, 1992). He used circle inversion in the complex number plane to study airfoil shapes.

4. 2011, David Salomon, The Computer Graphics Manual, https://books.google.com.au/books?id=DX4YstV76c4C&pg=PA88&dq=%22circle+inversion%22%7C%22circle+inversions%22&hl=en&sa=X&ved=0ahUKEwiDzsTgs9fNAhURNpQKHU-3BE0Q6AEIKTACv=onepage&q=%22circle%20inversion%22%7C%22circle%20inversions%22&f=false page 88,

As is common with nonlinear projections, it is possible to come up with many variants of circle inversions.(..)An obvious (but perhaps not very useful) extension of circle inversion is sphere inversion, where the spaces inside and outside a sphere are swapped.

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