The second-order conclusion of the area of an ellipse focus triangle is an important theorem in mathematics, also known as the "double focus triangle area theorem". It was put forward by Italian mathematician Herminur Bronnosferro in AD 1759. He found that if the two focuses of an ellipse are connected into a straight line, the straight line will cut a triangle on the ellipse, and the ratio of its area to ellipse circumference is fixed, which is the second-order conclusion of the triangle area of the ellipse focus.
The second-order conclusion formula of the area of the ellipse focus triangle is: S=2*a*b*π, where a is the radius of the major axis of the ellipse, b is the radius of the minor axis, and π is the roundness.
This theorem also has a wide range of applications. For a regular ellipse, the radius of its major axis A is equal to the radius of its minor axis B, and the theorem becomes: S = 2 * A 2 * π. This conclusion, also called "parallel axis theorem", can be used to calculate the area product of an ellipse.
At the same time, this theorem can also be used to calculate the circumference of an ellipse. According to the theorem, ellipse circumference C=4*a*b*π, where a and b are the radii of the major axis and minor axis of an ellipse respectively.
In addition, the second-order conclusion of the triangle area of ellipse focus can also be used to calculate the curve length of ellipse. According to the theorem, the curve length of an ellipse is L=2*a*b*π, where a and b are the major axis radius and minor axis radius of the ellipse respectively.
In addition, the second-order conclusion of the triangle area of the ellipse focus can also be used to solve the distance between the two focuses of the ellipse. According to the theorem, the distance between the two focuses of an ellipse is d = 2 * √ (A 2-B 2), where A and B are the major axis radius and minor axis radius of the ellipse respectively.
The second-order conclusion of the triangular area of the ellipse focus can also be used to calculate some geometric characteristics of the ellipse. For example, the radius b of the short axis of the ellipse can be solved by the radius a of the long axis of the ellipse, the area s and the length l of the curve.
To sum up, the second-order conclusion of the area of the ellipse focus triangle is a very important mathematical theorem, which can be used not only to calculate the area, perimeter and curve length of the ellipse, but also to solve the distance between the two focuses of the ellipse and some geometric features of the ellipse, and has a wide range of applications in mathematics and geometric squares.