The See-Saw Lemma

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.

Draw a semicircle with base AE and center at O. Let the tangent line to the semicircle at D meet the perpendiculars drawn from A and E at B and F. Let G be the point of intersection of BE and AF. Let C be the projection of D onto AE. Then there are three results: (1) GC = GD, (2) CD is equal to the harmonic mean of AB and EF: and (3) AO and OE equal the geometric mean of AB and EF: .

[more]

Drag the brown point or the sliders to change the figure.

[less]

Contributed by: Jay Warendorff (March 2011)
Based on work by: Alexander Bogomolny
Open content licensed under CC BY-NC-SA


Snapshots


Details

For more information see See-Saw Lemma: What Is This About?.



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