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Bottema's theorem is a plane geometry theorem by the Dutch mathematician Oene Bottema (Groningen, 1901 - 1992).[1]
The theorem can be stated as follows: in any given triangle ABC, construct a square on any two adjacent sides, i.e. AC and BC. The midpoint of the line segment that connects the vertexes of the squares opposite to the common vertex of the two sides, point C, is independent of vertex C.[2]
Attention should be paid regarding the squares' construction. The theorem holds true when the squares are constructed in one of the following way:
- Looking at the figure, follow the triangle vertexes starting from the lower left vertex, point A, towards point C and then, from point C towards point B, and construct each square on the left hand side of each side of the triangle.
- Follow the triangle in the same way and construct each square on the right hand side of each side of the triangle.
References
- ^ Teun Koetsier (2007). Oene Bottema (1901–1992). Springer. pp. 61–68.
- ^ Shriki, A. (2011), "Back To TREASURE ISLAND", The Mathematics Teacher, 104: 658–664.