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# Napolean’s Theorem

Haoqi Jin

Haoqi Jin Napoleon's Theorem Napoleon's Theorem in the Real World. If we construct equilateral triangles on the sides of any triangle, the centers of those equilateral triangles themselves form an equilateral triangle. Napoleon Bonaparte (1769 to 1821) history An accomplished mathematician

Made frequent contributions to the Ladies’ Diary

His motive for requesting a proof of the theorem is unclear William Rutherford The Ladies’ Diary http://nrich.maths.org/1944 Theorem attributed to him

Emperor of France

Talent for mathematics Controversy: Did Napoleon discover the theorem? Scholars trace origins of the theorem to 1825, which was after his death

Numerous articles cast doubt on whether Napoleon discovered it Historical Record 1825 article in Ladies’ Diary by William Rutherford

First reference to theorem as Napoleon’s theorem was in 1911 English scholarly journal

Published annually in London(1704-1841)

Also known as Woman’s Almanack

Scientific queries and calendar information proof Notice that if we rotate the figure counter-clockwise through an angle of 2p/3 about the point "c", the triangle originally centered at "b" moves to the position originally occupied by the triangle centered at "d". Thus the line segments cb and cd are of equal length and make an angle of 2p/3. Likewise if we rotate the figure clockwise through an angle 2p/3 about the point "a", the triangle centered at "b" again moves to the position of the triangle at "d", so the line segments ab and ad are of equal length and make an angle of 2p/3. Consequently the line ac bisects the angles at "a" and "c", so the triangle abc has an angle of p/3 at each vertex, so it is equilateral (as is acd). Relates to Heron's Formula for the area of a triangle in terms of edge lengths. Also relates Van Aubel's Theorem. Napoleon's TheoremFull transcript

#### Transcript of Napolean’s Theorem

Haoqi Jin Napoleon's Theorem Napoleon's Theorem in the Real World. If we construct equilateral triangles on the sides of any triangle, the centers of those equilateral triangles themselves form an equilateral triangle. Napoleon Bonaparte (1769 to 1821) history An accomplished mathematician

Made frequent contributions to the Ladies’ Diary

His motive for requesting a proof of the theorem is unclear William Rutherford The Ladies’ Diary http://nrich.maths.org/1944 Theorem attributed to him

Emperor of France

Talent for mathematics Controversy: Did Napoleon discover the theorem? Scholars trace origins of the theorem to 1825, which was after his death

Numerous articles cast doubt on whether Napoleon discovered it Historical Record 1825 article in Ladies’ Diary by William Rutherford

First reference to theorem as Napoleon’s theorem was in 1911 English scholarly journal

Published annually in London(1704-1841)

Also known as Woman’s Almanack

Scientific queries and calendar information proof Notice that if we rotate the figure counter-clockwise through an angle of 2p/3 about the point "c", the triangle originally centered at "b" moves to the position originally occupied by the triangle centered at "d". Thus the line segments cb and cd are of equal length and make an angle of 2p/3. Likewise if we rotate the figure clockwise through an angle 2p/3 about the point "a", the triangle centered at "b" again moves to the position of the triangle at "d", so the line segments ab and ad are of equal length and make an angle of 2p/3. Consequently the line ac bisects the angles at "a" and "c", so the triangle abc has an angle of p/3 at each vertex, so it is equilateral (as is acd). Relates to Heron's Formula for the area of a triangle in terms of edge lengths. Also relates Van Aubel's Theorem. Napoleon's Theorem