"Helen formula" was learned in the second grade of junior high school. Helen's formula has been translated into Hilong formula, Hailong formula, Hilo formula and Helen-Qin Jiushao formula. It is a formula for directly calculating the area of a triangle by using the side lengths of three sides of the triangle. The expression is: S=√p(p-a)(p-b)(p-c), which is characterized by beautiful form and easy memory. According to legend, this formula was first drawn by the ancient Greek mathematician Archimedes. Because this formula first appeared in Helen's book Geodesy, it was called Helen's formula.
Speaking of Helen, adding the word ancient Greece reminds me of a great beauty-the most beautiful woman in the world in the Trojan War, Helen. This is a Greek fairy tale. I only remember the 10 war between the Golden Apple, the Greek gods and Troy. In Homer's epic, Helen's beauty is not described in the front, but in the side. In the ninth year of the war, the Greek allied forces Enemy at the Gates and Troy were in danger. The elders of Troy sat on the rostrum, and Helen came to the rostrum. They talked about fighting such a war for such a beautiful woman. Such a beautiful woman is really charming.
Unfortunately, Helen mentioned today is not a beauty, not even a woman, but a man. The picture on the Internet is a bearded man. Helen's life is unknown. Presumably, she lived in Greece around 62 AD. She probably taught mathematics and physics in Alexandria, and was an ancient Greek mathematician, mechanic and mechanic.
His works include metrology, weapons manufacturing, measuring instruments, gas mechanics, automatic mechanism technology, definition, geometry, measurement, volume determination and so on. Surprisingly, they are rarely lost. Metrology was originally thought to be lost, but in 1896, German R.Schone found his manuscript of Metrology in Constantinople, which was revised and published by his son H. Schone in 1903, and the proof of Helen's formula was recorded in the second volume of this book.
Many fuzzy times in history can be recorded through literature, and the specific time of solar eclipse at that time can be inferred. Sometimes time is so wonderful and regular. When we find the Helen formula of triangle, some people will want to extend it to quadrilateral, pentagon, hexagon and even N-polygon. However, we all know that quadrangles are unstable, even pentagons and hexagons are unstable.
When we calculate the area of a quadrilateral, we must add other restrictions, such as angles or diagonals.
The history of Helen's theorem
This theorem was deduced by the ancient Greek mathematician Archimedes, but it is usually named after the ancient Greek mathematician Helen. This formula is called Helen formula because it first appeared in Helen's geodesy and was proved in Helen's book Measuring Instruments and Metrology.
Qin Zai 1247, a mathematician in Song Dynasty in China, independently put forward "tridiagonal quadrature". Although different from Helen's theorem in form, it is completely equivalent to Helen's theorem. It fills a blank in the history of Chinese mathematics, from which we can see that the level of ancient mathematics in China is very high.