What is Seeva s theorem What is Heine s theorem?

Seva's theorem: Let o be any point in abc, and ao, bo, and co intersect opposite edges to n, p, and m, respectively, then am mb*bn nc*cp pa=1

sin 1sin 3sin 5 = sin 2sin 4sin 6 (angular element Seva's theorem).

5 + 6 = 180-18-54-42-30 = 36 solve the above equation to get 5, 6

5 is what is sought.

Heine's theorem is a bridge between the limits of a sequence and the limits of functions.

Heine's theorem The sufficient and necessary conditions for the existence of lim[x->a]f(x)=b are: for any series of numbers that belong to the domain defined by the function f(x), and lim[n-> an = a, an≠a, there is lim[n-> f(an)=b.".Heine's theorem is a bridge between the limit of the communication function and the limit of the sequence.

According to Heine's theorem, finding the limit of a function can be reduced to finding the limit of the sequence.

Although the limits of the sequence and the limits of the function are defined separately, they are related. Heine's theorem profoundly reveals the relationship between the whole and the part, the continuous and the discrete of the variable changes, thus building a bridge between the limit of the sequence and the limit of the function. It states that the limit of a function can be reduced to the limit of a sequence and vice versa.

Heine's theorem plays an important role in limit theory. With Heine's theorem, all theorems about the limits of functions can be proved with the help of theorems that know the limits of the corresponding sequences.

Heine's theorem describes the connection between a sequence of numbers and a function. If the sequence n is infinite, then the value of the function tends to be fixed.

The inverse theorem is derived from the combination of the Syva theorem with the principle of uniqueness. That is to say, for example, if you already know that the product of three proportions is 1, when you want to prove that the three lines have a common point, you first assume that the two lines intersect at a certain point, and then use this point to have an intersection point with another fixed-point line and the third edge, and then use Syva's theorem to get a formula with a product of 1. And two of the proportional terms are the same, so we know that the third proportional term is the same, and the sum of the numerator and denominator is combined to obtain the uniqueness, and then the inverse theorem of Sayva is true.

And here your proportional term bf cf is the difference between the numerator and the denominator is a definite value, not the sum is a definite value, so it is not the same thing as the inverse theorem of Sayva. There is no contradiction. At the same time, if you use this difference as a fixed value, you can use the property of the ratio of fractions to obtain the uniqueness and obtain the inverse theorem of Menelaus's theorem.

Remember the inverse of the Sayva reason that the Seewa theorem combines the principle of uniqueness to introduce its inverse theorem, and Menelaus's theorem can also combine uniqueness.

Menelaus' theorem is the case where a straight line crosses three points.

Sayva's theorem is a case where three straight lines intersect at a point.

Although the form is the same, the conditions for application are clearly different.

The big difference is that the Seva tube is a three-point collinear tube, while Menelaus tube is a three-point colinear. Formally, both have a common form and an angular form. Menelaus is a little less limited, as long as there are an odd number of points on the extension of the triangle (i.e. it can be completely outside the triangle!). Seva's theorem does not mention that there can be a form outside the form, (maybe there is, but I haven't seen it). In terms of use, proving trilinear Menelaus is a very common method, but Seva is not a highly used method of proving trilinear co-point, and the same method is mostly used to prove trilinear co-point, as well as some more ingenious cases. It's been a long time since I left high school, and the things I don't know are very accurate, so come on, classmates!