 # Trisecting an Angle Using Tschirnhaus's Cubic

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.

This Demonstration illustrates a property of Tschirnhaus's cubic, which has polar equation . Namely, that the angle between the tangent and the normal to the radius vector at a given point on the curve is one-third of the polar angle of the point.

[more]

To trisect a given angle , draw the radius vector (red) from the origin, making that angle with the axis, to meet at a point on the curve. Construct the tangent (green) and the normal to the radius vector (green) at the point. The angle between these two lines is . So the angle is .

[less]

Contributed by: Izidor Hafner (January 2013)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

The curve is also known as Catalan's trisectrix or l'Hospital's cubic.

## Permanent Citation

Izidor Hafner

 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