Euclidean Theorem

Euclidean's law is a basic theorem in mathematics, which describes the relationship between the three sides of a right triangle.

Projection theorem, also known as Euclid's theorem: In a right triangle, the height of the hypotenuse is the middle term of the ratio of the projection of the two right-angled sides on the hypotenuse, and each right-angled side is this The projection of a right-angled side on the hypotenuse and the median term of the ratio of the hypotenuse. Projection theorem is an important theorem of mathematical graphics calculation.

Because projection is to scale the length of the original figure (height in a triangle), the width remains unchanged, and because the area ratio of a plane polygon = the product ratio of the side lengths. So it is the ratio of the length of the figure (height in a triangle). Then the ratio should be the cosine of the angle formed by the plane.

Construct a right triangle in two planes, and make the hypotenuse and the right side perpendicular to the edge (that is, the intersection of the plane of the original polygon figure and the projective plane), then the hypotenuse of the triangle and the other The right-angled side is the length ratio of its polygon, which is the area ratio of the plane polygon. The proof can be obtained by putting this ratio into a triangle in the plane.

Euclide (Greek: Ευκλε?δη?, 325 BC - 265 BC), an ancient Greek mathematician, is known as the father of geometry. He was active in Alexandria during the period of Ptolemy I (323 BC - 283 BC).

Projective geometry

As an ancient and exquisite branch of geometry, projective geometry originated in the 17th century. During this period, two outstanding mathematicians, étienne Desargues and Blaise Pascal***, both made pioneering contributions to the development of projective geometry. .

Projective geometry, as an ancient and sophisticated branch of geometry, explores the invariant properties of shapes when points are projected onto lines or planes. It is not only widely used in practical fields such as aviation, photography and surveying, but also has profound theoretical connotations.