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Anonymous users2024-02-07The only rule is that they all satisfy the Pythagorean theorem, where the square of two decimal places is equal to the square of a large number.
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Anonymous users2024-02-06Summary of the law of Pythagorean numbers: A positive odd number (except 1) with two consecutive positive integers whose sum is equal to the square of the positive odd number is a set of Pythagorean calendar numbers. Let n be a positive odd number (n≠1), then a set of Pythagorean numbers with n as the minimum value can be:
n、(n²-1)/2、(n²+1)/2。
The Pythagorean number, also known as the Pythagorean number. The Pythagorean number is a group of positive integers that can be constructed into three sides of a right-angled triangle. Pythagorean theorem: The sum of the squares of two right-angled sides A and B of a right triangle is equal to the square of the hypotenuse c (a + b = c).
Nature of the Pythagorean number:
1.The number of Pythagorean numbers is divided into two categories, the number of coprime Pythagoreans and the number of non-copied Pythagoreans.
The number of coprime Pythagorean numbers means that a, b, and c have no common factor.
The number of non-mutic Pythagorean is a multiple of the number of mutual Pythagorean.
2.The number of coprime Pythagorean numbers in the format of KitKat split number + even number = odd number
The general formula for coprime Pythagorean numbers is a,b,c= n -m,2nm,n +m,nm are positive integers,n>m,n,m coprime, n+m= odd number.
The formula for the Pythagorean number term is:
a,b,c= 2knm, k(n-m) k(n +m) k,n,m are any positive integers, n>m
There are only two kinds of Pythagorean numbers, odd + even = odd and even + even = even.
The general term formula means that given any set of Pythagorean numbers a, b, and c, the ternary equation can be solved to obtain the unique value of k, n, and m (n, m coprime), and vice versa.
3.The number of coprime Pythagoreans, a can be any odd number (excluding 1), b can be a multiple of any 4, c can be [a multiple of 4 + 1, and is a prime number] and their product.
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Anonymous users2024-02-05The Pythagorean theorem combines sum and sum and and .
If the length of the two right-angled sides of a right-angled triangle is a and b respectively, and the length of the hypotenuse is c, then it can be expressed mathematically: a +b = c, and all the numbers that meet this formula can become a combination of numbers for the Pythagorean theorem.
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Anonymous users2024-02-04The Pythagorean theorem has the following figures:
There are seven groups of fundamental numbers, which are , these are even numbers, and these are odd numbers. No matter how many times it is expanded, these have a common divisor, and they are all mutually primary.
Introduction to the Pythagorean theorem:
Zhou Ji shouted Feng Sutra records: In the early years of the Western Zhou Dynasty, Shang Gao proposed "hook three strands, four strings and five". This is a special case of the Pythagorean theorem.
The Pythagorean theorem is that the area of a square on the hypotenuse of a right triangle is equal to the sum of the areas of the two squares on the right angle. In ancient China, two right-angled sides were called hooks and strands, and hypotenuse edges were strings. Hook three strands, four strings, five is:
The square nine of the hook three, and the square sixteen of the four strands, is equal to the square of the string five twenty-five. It shows that China has mastered the Pythagorean theorem very early, and Greece in the West did not discover this theorem until Pythagoras in the sixth century BC.
Practical uses of the Pythagorean theorem:
1. The Pythagorean theorem understands triangles.
2. The Pythagorean theorem and the grid problem.
3. Use the Pythagorean theorem to solve the folding problem.
4. Li Zheng Hongsheng used the Pythagorean theorem to prove the square relationship of line segments.
5. Use the Pythagorean theorem to solve practical problems - find the height of the ladder slide.
6. Use the Pythagorean theorem to solve the actual problem - find the height of the flagpole.
7. Use the Pythagorean theorem to solve practical problems - find the crawling distance of ants.
8. Use the Pythagorean theorem to solve practical problems - find the height of the tree before it breaks.
9. Use the Pythagorean theorem to solve practical problems - find the length of chopsticks in a water cup. <>
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Anonymous users2024-02-03The Pythagorean number, also known as the Pythagorean number. The Pythagorean number is a set of positive integers that can form the three sides of a right triangle. Pythagorean theorem: The sum of the squares of two right-angled sides A and B of a right triangle is equal to the square of the hypotenuse c (a + b = c).
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Anonymous users2024-02-02Categories: Education Academic Exams >> Study Help.
Analysis: In a right-angled triangle, if a and b represent two right-angled edges, and c represents hypotenuse, the Pythagorean theorem can be expressed as a2+b2=c2.
The positive integers a, b, and c satisfying this equation are called a set of Pythagorean numbers.
For example, each group can satisfy a2+b2=c2, so they are all Pythagorean arrays (where is the simplest set of Pythagorean numbers). Obviously, if the sides of a right triangle are positive integers, then these three numbers form a set of Pythagorean numbers; Conversely, each set of Pythagorean numbers determines a right triangle with a positive side length of an integer. Therefore, mastering the method of determining the Pythagorean array is of great significance for the study of right triangles.
1 Take any two positive integers m, n, so that 2mn is a perfectly squared number, then.
c=2+9+6=17。
is a set of Pythagorean numbers.
Proof: a, b, and fissure front do c to form a set of Pythagorean numbers.
2 Take any two positive integers m, n, (m n), then.
A=M2-N2, B=2Mn, C=M2+N2 form a set of Pythagorean numbers.
For example, when m=4, n=3, a=42-32=7, b=2 4 3=24, c=42+32=25
is a set of Pythagorean numbers.
Proof: a2+b2=(m2-n2)+(2mn)2
m4-2m2n2+n4+4m2n2
m4+2m2n2+4n2
m2+n2)2
C2 a, b, c form a set of Pythagorean numbers.
3 If one of the numbers in the Pythagorean array has been determined, the other two numbers can be determined as follows.
Start by observing whether a known number is odd or even.
1) If it is an odd number greater than 1, it is squared and split into two adjacent base integers, then the odd number and these two integers form a set of Pythagorean numbers.
For example, 9 is a number in the Pythagorean number, then is a set of Pythagorean numbers.
Proof: Let an odd number greater than 1 be 2n+1, then square it and split it into two adjacent integers.
2) If it is an even number greater than 2, divide it by 2 and then square it, and then subtract 1 from this square number respectively, and add 1 to obtain two integers and this even number to form a group of Pythagorean numbers.
For example, 8 is a number in the Pythagorean array.
Then, 17 is a set of Pythagorean numbers.
Proof: Let the even number 2n greater than 2, then divide the even number by 2 and then square it, and then subtract the square number by 1 respectively, and add 1 to get the two integers n2-1 and n2+1
2n)2+(n2-1)2=4n2+n4-2n2+1
n4+2n2+1
n2+1)2
2n, n2-1, n2+1 make up a set of Pythagorean numbers.
In China, the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse is called the Pythagorean theorem or the Pythagorean theorem, also known as the Pythagorean theorem or Pythagoras theorem. In mathematical formulas, it is often written as a +b =c >>>More
The sum of the squares of the two right-angled edges is equal to the sum of the squares of the hypotenuses.
Proof 2 can be considered a very straightforward proof. The most interesting thing is that if we flip the right triangle in the diagram and put it together in Figure 3 below, we can still use a similar method to prove the Pythagorean theorem.
If the three sides of a triangle are related to the lengths a, b, and c, then the triangle is a right triangle." This proposition is called the inverse theorem of the Pythagorean theorem. >>>More
Einstein and the Pythagorean theorem[1] Wang Bonian, Song Limin, Shi Zhaoshen (University of Shanghai for Science and Technology, Shanghai 200093, China) [Abstract] Based on the analysis of reliable and original biographical materials of Einstein, Einstein's "Autobiography" and Euclid's "Geometric Primitives", it can be confirmed that Einstein independently came up with a proof of the Pythagorean theorem when he was 12 years old, and this is the simplest and best of the many proofs. However, this is not innovative, as it is present in the Geometry Originals. Einstein's natural curiosity, keen rational thinking, diligent inquiry, and the education of the enlighteners were necessary for this miracle to happen. >>>More