Inversive Geometry IV: Inverting a Point with a Compass in Three Steps

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Given a point Z and an inversion circle with center at point Q and radius , consider the following construction to obtain the inverse Z' of Z in . Draw the circle centered at Z passing through Q; let it intersect at points A and B. Draw two circles and centered at A and B both passing through Q. Their second point of intersection is the inverse of Z in . We justify this by the following reasoning: if we invert and in we obtain (red dotted) lines passing through Z; these lines intersect at and Z, hence their inverses must intersect at the inverses of and Z, namely Q and Z'. This Demonstration lets you drag the point Z (red); the construction works for all points Z at a distance from Q greater than .

Contributed by: Jaime Rangel-Mondragon (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send