File:Sallows triangle theorem.svg
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Summary
| Description | Visual proof of Lee Sallows's triangle theorem by CMG Lee. 1. Lines from midpoints of edges of length a, b and c (circles) to the opposite vertex split the triangle into 6 regions. 2. Each region is rotated 90 degrees outwards about its hinge, yielding 3 congruent triangles with sides equal and perpendicular to the line segments between the original triangle's vertices and its centroid (2x, 2y and 2z). 3. The process can be repeated on each smaller triangle. 4. Each resulting triangle has sides a/3, b/3 and c/3, similar to but 1/9 the area of the original. |
| Source | Own work |
| Author | Cmglee |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:47, 4 March 2024 | | 512 × 512 (10 KB) | Cmglee | {{Information |Description=Visual proof of Lee Sallows's triangle theorem by CMG Lee. 1. Lines from midpoints of edges of length ''a'', ''b'' and ''c'' (circles) to the opposite vertex split the triangle into 6 regions. 2. Each region is rotated 90 degrees outwards about its hinge, yielding 3 congruent triangles with sides equal and perpendicular to the line segments between the original triangle's vertices and its centroid (2''x'', 2''y'' and 2''z''). 3. The process can be repeated on each s... |
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