Proposition 1 in Taxicab Geometry
Euclid proved you can construct an equilateral triangle using the intersection of two circles:
- Draw line segment AB
- Create a circle centered at A with radius AB
- Create a circle centered at B with radius AB
- Find the intersection of the two circles and call it C
- Create segments AC and BC
- Triangle ABC is equilateral.
Does the construction work to create a taxi-equilateral triangle? How do you know?
If it does create an equilateral triangle, does it hold all the same properties as a Euclidean equilateral triangle? If it doesn't, are there any similarities between this triangle and and Euclidean equilateral triangle?