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There are three major problems in the drawing of rulers in Euclidean geometry, which are said to have been "solved". However, there are still many people who continue to study these three difficult problems of geometry, why is that? Are these people "daydreaming"?
No! The so-called "solution" to the three major problems of geometry is the "algebraic method". This "algebraic method" uses a criterion of "starting from a known rational number, and giving the number by finite addition, subtraction, multiplication, division, and squarering".
However, when explaining the possibility of "bisecting an arbitrary angle", we can only use the criterion of "the known number is the number given by a finite number of addition, subtraction, multiplication, division, and squared". Comparing the two criteria, they differ only by the word "reasonable". If both discriminant criteria can be used in the drawing of rulers, then these two (double) discriminant criteria constitute a mathematical paradox, which impacts the foundation of mathematics, or this mathematical paradox tortures the certainty of the mathematical foundation, which is a mathematical content that causes headaches in the mathematical community.
The mathematical paradox gave those mentioned above the opportunity to continue their study of the three major puzzles of geometry. This is a research group that cannot disappear at present, and the number of this research group is likely to only increase, so ruler drawing is a mathematical content with research value and research prospects, and the Chinese are continuing to study Euclidean geometry (or the "shape" part of mathematics) in their own way.
I hope that Mr. Yau Chengtong can see the above content and guide the middle school students correctly.
If there is even a slight amount of reasonableness in the above content, please spread the word among the students, thank you.
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This one. I only know the last two.
18. Lobachevsky.
20. Andrew Wiles, Fields Medal Special Award.
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The first work on the history of mathematics was "The History of Mathematics and Fibers" written by ().
a.Archimedes.
b.Monticra.
c.Warris.
d.Zu Chongzhi.
Correct answer: B
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The history of <> mathematics can be roughly divided into four stages.
The first period of mathematics is the formative period, which is the period when mankind establishes the most basic mathematical concepts. Human beings have gradually established the concept of natural numbers, simple calculations, and recognized the most basic and simple geometric forms, and arithmetic and geometry have not been separated.
The second period of elementary mathematics, that is, the period of constant mathematics. The basic and simplest results of this period constitute the main content of secondary school mathematics today. This period began in the 5th century BC and perhaps earlier, until the 17th century, and lasted for about two thousand years.
This period gradually formed the main branches of elementary mathematics: arithmetic, geometry, algebra, trigonometry.
The third period, the period of variable mathematics. The mathematics of variables arose in the 17th century and went through two decisive and major steps: the first was the emergence of analytic geometry; The second step is calculus [Calculus is the branch of mathematics in advanced mathematics that studies the differentiation and integration of functions, as well as related concepts and applications.
It is a fundamental subject of mathematics. The content mainly includes limits, differential calculus, integral science and their applications. Differential calculus consists of the operation of finding derivatives and is a set of theories about the rate of change.
It makes it possible to discuss functions, velocities, accelerations, and slopes of curves in a common set of notations. Integralism, including the operation of finding integrals, provides a general set of methods for defining and calculating area, volume, etc. ] of the founding.
Fourth Period Modern Mathematics. The period of modern mathematics began roughly in the first half of the 19th century. The beginning of the modern phase of the development of mathematics is characterized by profound changes in all its foundational --- algebra, geometry, analysis.
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Thales, Pythagoras, Euclid, Archimedes, Apronias, Zeno, Ptolemy, Hypatia.
Gauss, Leibniz, Hilbert, Cantor, Klein, Riemann, Ratmacher, Amy Noether, Dirichlet, Courant.
Lagrange, Laplace, Pierre Fermat, Cauchy, Poisson, Gardan, Galois, Fourier, Marie-Sophie Germain, Grosendijk, Poincaré.
Euler, Nicolas Bernoulli, Daniel Bernoulli, Jacob Bernoulli, John Bernoulli von Neumann.
Kolmolokov, Fibonacci, Pontriagin, Rugin, Arnold, McLaughlin.
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Gauss, Leibniz, Hilbert, Cantor, Klein, Riemann, Ratmacher, Amy Knott, Dirichley, Courant, Zermelo Descartes, Newton, Taylor, McLaughlin.
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Many of the results of mathematics were obtained long ago, and knowing this is important to determine what exactly is to be learned in mathematics, and of course it is equally important to be taught in mathematics.
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First of all, it should be noted that the first number of each card, the first number of the four cards here is 2 0, 2 1, 2 2, 2 3.
Then, let's say I select n as 13, then look closely and see that the number 13 is on the first, third, and fourth cards.
Then I just need to tell someone that the number I chose is on the 1st, 3rd and 4th cards, then they can add up the number 1 in the upper left corner of the first card, the number 4 in the upper left corner of the third card, and the number 8 in the upper left corner of the fourth card
The meaning of binary is every two into one, such as 13 = 1 + 4 + 8 = 2 0 + 2 1 + 2 2 = 1101 (corresponding to the first, third and fourth digits of the binary number from low to high, If there are n cards, then you can know that a total of (2 n -1) numbers can be guessed, and the first number of each card is 2 (n-1).
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