2. Historically, the geometric derivation methods of sine theorem are rich and colorful. According to its thinking characteristics, it can be mainly divided into two types.
3. The first method, which can be called "Equal Diameter Method", was first adopted by Arab mathematician and astronomer Nasir Ear Nail in the 3rd century A.D./Kloc-0 and German mathematician Ragio Montanus in the 5th century A.D./Kloc-0. "Equal Diameter Method" regards the sine of two internal angles of a triangle as a sine line on a circle with the same radius (before16th century, trigonometric function was regarded as a line segment instead of a ratio), and the ratio of the two is equal to the ratio of the opposite sides of the angle by using similar triangles property. Nasir Din extends to the opposite sides of two internal angles at the same time, and the structural radius is larger than the circles on both sides. Reggiomontanus simplified Nasir al-Din's method, and only extended the shorter of the two sides to construct a circle with the same radius as the longer one. From 17 to 18, China mathematician and astronomer Mei Wending and British mathematician Simpson independently simplified the "equal diameter method".
4./kloc-At the beginning of 0/8th century, "equal diameter method" evolved into "right triangle method". This method does not need to select and make the radius of a circle, but only needs to make the height line of a triangle, and the sine theorem can be obtained by using the angular relationship of a right triangle. 19th century, the British mathematician Woodhouse began to uniformly take R= 1, which is equivalent to expressing trigonometric functions by ratios, and obtained the "height method" widely used today.
5. The second method is "circumscribed circle method", which was first adopted by the French mathematician Veda in16th century. David did not discuss the obtuse triangle, which was supplemented by later mathematicians.