Yang Hui's triangle also corresponds to the coefficient of binomial theorem. The binomial coefficient of degree n corresponds to the n+ 1 line of Yang Hui triangle. For example, in, the quadratic binomial just corresponds to the coefficient 1 2 1 of the third line of Yang Hui Triangle.

Yang Hui triangle consists of positive integers, and the numbers are symmetrical. Each line starts at 1, gradually becomes larger and smaller, and returns to 1. The number in the n-th row is n, and the k-th number in the n-th row is a combination number.

Yang Hui triangle is a geometric arrangement of binomial coefficients in triangle. In Europe, this watch is called Pascal Triangle. Pascal (1623- 1662) discovered this rule in 1654.

It is 393 years later than Yang Hui and 600 years later than Jia Xian. Yang Hui Triangle is one of the outstanding research achievements of ancient mathematics in China. It displays binomial coefficients graphically, and intuitively reflects some algebraic properties of combination numbers. It is a combination of discrete numbers and shapes.

Extended data:

Power consumption reduction formula:

1、sin^2(α)=( 1-cos(2α))/2=versin(2α)/2

2、2cos^2(α)=( 1+cos(2α))/2=covers(2α)/2

3、tan^2(α)=( 1-cos(2α))/( 1+cos(2α))

Derived formula:

1、 1tanα+cotα=2/sin2α

2、tanα-cotα=-2cot2α

3、 1+cos2α=2cos^2α

4、、4-cos2α=2sin^2α

5、 1+sinα=(sinα/2+cosα/2)^2=2sina( 1-sin2a)+( 1-2sin2a)sina

Sum and difference of two angles:

1、 1cos(α+β)= cosαcosβ-sinαsinβ

2、cos(α-β)=cosα cosβ+sinα sinβ

3、sin(α β)=sinα cosβ cosα sinβ

4、4 tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)

5、tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)

Baidu Encyclopedia-formulas of trigonometric functions

Baidu Encyclopedia-Yang Hui Triangle