Today, there is a pool of ten feet, born in the center, and one foot out of the water. Lead it ashore, and it will be suitable for landing. What is the water depth and the geometry of the water depth?
A: The water depth is one foot and two feet; This scab is one foot three feet long.
Technically, it is said: half a pool is self-multiplied, one foot is self-multiplied, and the rest is divided by twice the water, that is, the water depth is obtained. Add water, and it will grow.
Pythagorean theorem:
There is a ten-foot pool with reeds in the middle, which is one foot above the water. Drag the reeds to the shore, just in time to reach the shore. How deep is the water and how high is the reed?
A: The water depth is one foot two feet, and the reed is one foot three feet high.
Calculation method: Fold the side length of the pool into half a square, add the square of hydraulics, and subtract the sum of the former from the square of reed height to calculate the water depth, and add one foot to reed height.
That is, if the water depth is x and the reed height is (x+0. 1), there are:
2. English translation of ancient Chinese translation "Bamboo is one foot high and eventually falls to the ground, three feet away. Why is bamboo still tall? " There was a bamboo ten feet high. The tip of the bamboo broke and fell to the ground. The distance between the bamboo tip and the bamboo root is three feet. How high is the trunk? Let the apex of bamboo be A and the root end point be B, and break from C, then point A falls to the ground and there is a right triangle ABC, where B is the right angle and AC is the hypotenuse. According to the conditions, AC+BC= 1 foot = 10 foot and AB=3 feet, the length of BC is obtained. According to Pythagorean theorem, the equation can be listed as: BC 2.
3. Solve the Pythagorean Theorem problem (there is an answer), and all kinds of problems can be 1. In △ABC, a=(m+n) squared-1, b = 2m+2n, and c = (m+n) squared+1. Try to judge the shape of △ABC.
2. Given that AD is the height of △ABC, AD = the square of BDDC, is △ABC a right triangle? Explain why.
3. The ratio of the three internal angles of a triangle is 1:2:3, and its largest side is m, so what is its smallest side?
4. What is the area of an isosceles right triangle with the hypotenuse height m?
1. In △ABC, a=(m+n) squared-1, b = 2m+2n, and c = (m+n) squared+1. Try to judge the shape of △ABC.
Solution: 2 is a square and 4 is a power of 4.
a^2=(m+n)^4-2(m+n)^2+ 1
b^2=4(m+n)^2
c^2=(m+n)^4+2(m+n)^2+ 1
b^2=c^2-a^2
So the triangle is a right triangle.
2. Given that AD is the height of △ABC, AD = the square of BDDC, is △ABC a right triangle? Explain why.
Solution: △ABC is a right triangle, and 2 represents a square.
Derived from ad 2 = BD DC
AD/BD=DC/AD
Because AD is perpendicular to BC
So △ △ADB is similar to△△△ CDA.
So angle ABD= angle CAD angle BAD= angle ACD,
Because angle ADB= angle ADC=90 degrees
So angle ABD+ angle BAD=90 degrees.
So angle BAD+ angle CAD=90 degrees.
So a triangle is equivalent to a right triangle.
3. The ratio of the three internal angles of a triangle is 1:2:3, and its largest side is m, so what is its smallest side?
According to sine theorem, the minimum edge is 0.5m
4. What is the area of an isosceles right triangle with the hypotenuse height m?
Solution "
It is found that the bottom length is 2m,
S=0.5*m*2m=m*m
Please punctuate the following two classical Chinese math problems and write the answers, 1 triangle geometry octagonal triangle three. First of all, what you entered may be wrong: triangle geometry * * octagon, triangle triangle, geometric geometry triangle+geometry = octagonal triangle = triangular money, so geometry = fifty cents. So the answer is: five cents is nine feet high, so it belongs to the book. ? Bamboo is broken, but not broken. The top (the end refers to the treetop) touches the ground and forms a right triangle with the remaining stumps planted in the soil and the ground. In which the oblique folding part is the hypotenuse C, the lower section of bamboo stands upright as the right-angled side B, and the bamboo on the ground is the other right-angled side A, where c+b=9 and a=3. Pythagorean theorem c set? -B? =3? =9，get (C+B) (C-B) = 9，C-B = 9/(C+B) = 9/9 = 1。 From the simultaneous equations of c+b=9 and c-b= 1, it is found that b=4 feet is an upright bamboo trunk.
5. Ask for help in translating the classical Chinese "Zhou Kuai Suan Jing". Zhou Kuai Suan Jing is one of the ten classic books of calculation. It was written in 1 century BC and was originally named Zhou Xie. It is the oldest astronomical work in China, which mainly expounds the theory of covering the sky and the method of seasonal calendar at that time. In the early Tang Dynasty, it was stipulated as one of imperial academy's teaching materials, so it was renamed Zhou Kuai. The main achievement of Zhouyi ·suan Jing in mathematics is the introduction of Pythagorean theorem and its application in measurement. The original book did not prove Pythagorean theorem, but the proof was given by Zhao Shuang in Zhou Zhuan Pythagorean Notes.
One of China's earliest works on mathematics and astronomy. In ancient China, there were three kinds of astronomical theories according to different universe models, among which Gai Tian Shuo was one kind, and Zhouyi Tian Jing was the representative. The theory of this school holds that the sky is like a hat and the earth is like an overturned basin (the sky is like a hat and the earth is like an overturned basin).
According to textual research, Zhou pian Shu Jing was written in the Western Han Dynasty (BC 1 century). The block-printed edition of Southern Song Dynasty (Jiading 6th year, 12 13) is the earliest block-printed edition handed down at present, and it is collected in Shanghai Library. Many mathematicians in the past dynasties have annotated this book, the most famous of which is the annotation by Feng Chun and others in the Tang Dynasty. The classic of parallel week calculation has also spread to South Korea and Japan, where there are also many inscriptions.
Judging from the content of mathematics, the book mainly tells the method of learning mathematics, using Pythagorean theorem to calculate abstruse distance and complex fraction calculation.
There are mathematical contents in the book, such as the use of moments (tools for measuring right angles and drawing rectangles), Pythagorean theorem and its application in measurement, and the proportional theorem of corresponding sides of similar right triangles.
There are also the problems of square root and arithmetic progression, complicated fractional algorithm and Kaiping method, complicated fractional operation applied to the calculation of ancient "quarter calendar", complicated numerical calculation and the application of Pythagorean theorem.
The first chapter of the book describes the measurement method of Pythagorean theorem mentioned by Zhou Gong and Shang Gao in their questions and answers, and also gives a special case of "three strands, four strings and five".