黄幂 = (勾股 - 股勾) × (勾股 - 股勾) = (b - a)^2
about 朱幂 and 黄幂 :
about 朱幂 and 黄幂 here are names representing variables in the illustration.
朱 and :黄 each represent a color, and 幂 represents the area of a certain figure.
The eight 幂朱幂 meansin the illustration refer to the eight right triangles.
The 自乘黄幂, its explanation refers to the middle square.
The 弦幂 I mentioned is abovea variable representing the large square around the perimeter.
The value of 朱幂 is the value of the area of the right triangle.
The value of 黄幂 is the value of the area of the small square in the middle.
The value of 弦幂 is the sum of four 朱幂 and one 黄幂.
In the picture I provided, the new variable
勾股差幂refers to黄幂.
勾股差幂can better express the meaning of this small square.Its value is the square of the result obtained by subtracting the value of
勾from the value of股.
As can be seen from the pictureillustration provided by the questioner:
about 朱幂 and 黄幂 :
幂 means 自乘, its explanation is above.
As can be seen from the picture:
about 朱幂 and 黄幂 :
朱幂 and 黄幂 here are names representing variables in the illustration.
朱 and 黄 each represent a color, and 幂 represents the area of a certain figure.
The eight 朱幂 in the illustration refer to the eight right triangles.
The 黄幂 refers to the middle square.
The 弦幂 I mentioned is a variable representing the large square around the perimeter.
The value of 朱幂 is the value of the area of the right triangle.
The value of 黄幂 is the value of the area of the small square in the middle.
The value of 弦幂 is the sum of four 朱幂 and one 黄幂.
In the picture I provided, the new variable
勾股差幂refers to黄幂.
勾股差幂can better express the meaning of this small square.Its value is the square of the result obtained by subtracting the value of
勾from the value of股.
As can be seen from the illustration provided by the questioner:
The Pythagorean theorem(translation is 毕达哥拉斯定理) in ancient Chinese mathematics is called 勾股定理.
Typically, the mathematical expression we use to describe the Pythagorean Theorem is
a^2+b^2=c^2.
At the same time, we usually think of the hypotenuse of a right triangle as c, the short right side as a, and the long right side as b.
Therefore, a is shorter than b, and b is shorter than c.(a <= b, b < c)
Description of Pythagorean theorem in ancient Chinese mathematics
短面曰勾，长面曰股，相与结角曰弦。勾短其股，股短其弦。——《九章算术·勾股》
译文： 在直角三角形中，短的边称为勾，长的边称为股，与它们分别形成直角的边为弦。勾的长度比股短，股的长度比弦短。
In a right triangle, the short side is called
勾, the long side is called股, and the side forming a right angle with them is弦.
勾 is shorter than 股, and 股 is shorter than 弦.（勾 <= 股，股 < 弦）
Note that 冪 is the traditional Chinese character for 幂, and the 幂 mentioned below all refer to 冪.
"the product of two numbers" means
两数之积in Chinese. "multiplying"multiplying a number by itself" means
自乘（一个数与自身相乘）in Chinese.
Now go back to the Pythagorean theorem(毕达哥拉斯定理，勾股定理).
Typically, the mathematical expression we use to describe the Pythagorean Theorem is a^2 + b^2 = c^2.
At the same time, we usually think of the hypotenuse of a right triangle as c, the short right side as a, and the long right side as b.
Therefore, a is shorter than b, and b is shorter than c.(a <= b, b < c)
Description of Pythagorean theorem in ancient Chinese mathematics
短面曰勾，长面曰股，相与结角曰弦。勾短其股，股短其弦。——《九章算术·勾股》
译文： 在直角三角形中，短的边称为勾，长的边称为股，与它们分别形成直角的边为弦。勾的长度比股短，股的长度比弦短。
In a right triangle, the short side is called
勾, the long side is called股, and the side forming a right angle with them is弦.
勾 is shorter than 股, and 股 is shorter than 弦.（勾 <= 股，股 < 弦）
Now back to the question.
about 朱幂 and 黄幂 :
朱 means 赤色, indicate red.
朱，赤心木，松柏属。——《说文解字》
方幂 here means square, can be replaced by the word 幂自乘, its explanation is above.
Note that 冪 is the traditional Chinese character for 幂, and the 幂 mentioned below all refer to 冪.
"the product of two numbers" means
两数之积in Chinese. "multiplying a number by itself" means自乘（一个数与自身相乘）in Chinese.
Now go back to the Pythagorean theorem(毕达哥拉斯定理，勾股定理).
Typically, the mathematical expression we use to describe the Pythagorean Theorem is a^2 + b^2 = c^2.
At the same time, we usually think of the hypotenuse of a right triangle as c, the short right side as a, and the long right side as b.
Therefore, a is shorter than b, and b is shorter than c.(a <= b, b < c)
Description of Pythagorean theorem in ancient Chinese mathematics
短面曰勾，长面曰股，相与结角曰弦。勾短其股，股短其弦。——《九章算术·勾股》
译文： 在直角三角形中，短的边称为勾，长的边称为股，与它们分别形成直角的边为弦。勾的长度比股短，股的长度比弦短。
In a right triangle, the short side is called
勾, the long side is called股, and the side forming a right angle with them is弦.
勾 is shorter than 股, and 股 is shorter than 弦.（勾 <= 股，股 < 弦）
about 朱幂 and 黄幂 :
方 here means square, can be replaced by the word 幂.
The Pythagorean theorem(translation is 毕达哥拉斯定理) in ancient Chinese mathematics is called 勾股定理.
Typically, the mathematical expression we use to describe the Pythagorean Theorem is
a^2+b^2=c^2.
At the same time, we usually think of the hypotenuse of a right triangle as c, the short right side as a, and the long right side as b.
Therefore, a is shorter than b, and b is shorter than c.(a <= b, b < c)
Description of Pythagorean theorem in ancient Chinese mathematics
短面曰勾，长面曰股，相与结角曰弦。勾短其股，股短其弦。——《九章算术·勾股》
译文： 在直角三角形中，短的边称为勾，长的边称为股，与它们分别形成直角的边为弦。勾的长度比股短，股的长度比弦短。
In a right triangle, the short side is called
勾, the long side is called股, and the side forming a right angle with them is弦.
勾 is shorter than 股, and 股 is shorter than 弦.（勾 <= 股，股 < 弦）
Note that 冪 is the traditional Chinese character for 幂, and the 幂 mentioned below all refer to 冪.
"the product of two numbers" means
两数之积in Chinese."multiplying a number by itself" means
自乘（一个数与自身相乘）in Chinese.
Now back to the question.
about 朱幂 and 黄幂 :
朱 means 赤色, indicate red.
朱，赤心木，松柏属。——《说文解字》
幂 means 自乘, its explanation is above.