perplexus.info :: Geometry : Unit lengths and triangles

Unit lengths and triangles (Posted on 2009-09-09)

Given A=(1,0), B=(0,0), and C=(0,1)
find all unit length equilateral triangles XYZ such that the lengths AX, BY, and CZ are all one unit.

No Solution Yet Submitted by Jer

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Puzzle Thoughts

Comment 3 of 3 |

1. (1,1),(0,1),(1/2, 1+sqrt(3)/2)

2. (1+sqrt(3)/2,1/2),(1,0),(1, 1)

3. (1-sqrt(3)/2,1/2),(1,0),(1, 1)

4. (0,0),(sqrt(3)/2, -1/2),(sqrt(3)/2, 1/2)

5. (0,0),(0,1),(sqrt(3)/2,1/2)

6. (1,1),(0,1),(1/2, 1-sqrt(3)/2)

7. (1/2,sqrt(3)/2),(-1/2,sqrt(3)/2),(0,0)

8. (1/2,-sqrt(3)/2),(-1/2,-sqrt(3)/2),(0,0)

9. (0,0),(0,1),(-sqrt(3)/2,1/2)

10. (0,0),(-sqrt(3)/2,-1/2),(-sqrt(3)/2,1/2)

11. (1/2,sqrt(3)/2),(1,0),(0,0)

12. (1/2,-sqrt(3)/2),(1,0),(0,0)

Posted by K Sengupta on 2023-07-02 22:12:13

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