Euclid proved you can construct an equilateral triangle using the intersection of two circles: [br][br][list=1][*]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. [/*][/list][br]If we follow these same steps using taxi-circles, do we get a taxi-equilateral triangle? Carry out the construction below and determine whether it works or not.
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?