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Sort of Can You...Maybe Yes...Maybe No... #5

In how many ways can you divide an equilateral triangle into three parts, that shall be equal to each other, and similar to each other?



My Note: Assume that the "equal" means "equal in area"...do they have to be congruent as well? Plus, the animation (from the web site Visual Mathematics) suggests a way to break an equilateral triangle into four equal, similar parts...that are congruent.

Solution:

Source: W. Spencer's Inventional Geometry: A Series of Patterns, 1876, p. 47