Different forms of beauty have different descriptions: magnificent, handsome, beautiful, gentle and graceful, and mathematical beauty also presents diversity. We can divide it into beauty of simplicity, beauty of symmetry, beauty of harmony and beauty of strangeness. The beauty of simplicity is a kind of beauty that people appreciate most, and it is most common in art, architecture, logo and other designs. Chinese painting embodies the beauty of simplicity. Mathematics is famous for its simplicity! ? Representation of large numbers and decimals: 10 22 1, 2 86243, 10 -900? Representation of Numbers: All numbers can be represented by 1, 2, 3, 5, 6, 7, 8, 9, 0. (It's called Arabic numerals, but it was invented by Indians, and Arabs spread to the west. ) is of great significance in form and status. In fact, the emergence of 0 is probably hundreds of years later. 6 → 23 ∪ 6 → 2306 Simple and beautiful development process: 235×4=940 Roman algorithm: CCXXXV IV CCCCCCCCCCCCCCCCCCCCCCC XXXXXXXXXXXXXVVvv DCCC stands for 900 CMXL CXXXXX stands for 40 decimal and binary: decimal: 89 89 = 1 2+65438. +0× 2+1/kloc-0 /×+0× 2+1× 2 binary:1010013265438+but the system is more complicated. Binary: There are few symbols (2), which is troublesome to express and convenient for machine operation, but the system is simple. The combination of binary and the simplest natural phenomenon (the binary of the signal and the pole of the simplest natural phenomenon signal) creates a computer! Combine into a computer. The combination of two poles makes a computer! Simple beauty of other symbols: unknown quantity: x, y, z known quantity: π, e, a, b, c function relation: f(x) shape symbol: simple beauty of other symbols: d? ×÷ operation symbols:+,,,sin, cos,, dx F function and logic: function and logic: = 0? V = c, Newton's first law d F = (m v), Newton's second law dt m 1 m 2, law of universal gravitation F =k 2 r Geometry: point symmetry, line symmetry, plane symmetry and spherical symmetry. The sphere is considered the most perfect! Algebra and Function Theory: * * Yoke Number (* * Yoke Complex Number, * * Yoke Space). Operation: operation of exchange law, distribution law, function and inverse function. Yang Hui triangle formed by the coefficients in the binomial theorem expansion: Yang Hui triangle:1121331464115/. Proposition, inverse proposition, no proposition, inverse proposition, unity and harmony are another aspect of mathematical beauty, which is broader than symmetrical beauty. It is more extensive than symmetrical beauty. Take the harmonious unity of geometry and algebra as an example: the harmonious unity of algebra as an example: the row-column formula and the matrix plane pass through the point plane (x 1, y 1), (x2, Y2): the equation xx 1 x2y1y/kloc-0. Y 1 formula: ax+by+c = 0 The general form of all quadratic curves on the plane: ax+2bxy+cy+dx+ey+f = 0.22 Its properties and types depend on three quantities: h = a+c, δ = a b b c a b d,? = b d c e e f δ，？ Instead of constants, translation and rotation transformations are used. 1.？ ≠ 0，δ& gt； 0 is an ellipse; δ& lt； 0 is a hyperbola; δ =0 is a parabola. 2.=0，δ& gt； 0 is an ellipse; δ& lt； 0 is two intersecting straight lines; Δ = 0 Two parallel or coincident lines are strange: rare, unexpected and fascinating! 1 = 0. 166666666666666 L 6 1 = 0. 142857 142857 142857 142857 142857 L 7 98765432 / kloc-0/ = 8.000000007229 1 10 3 = 10 = 9 10 ∑ ? 10 ? 123456789 10 ? 9 1 n = 0？ 10 ? 3 ∞ n So 98765432 1？ 9 1 ? 3 ? 10 = 8 + 9 10 ∑ ? 10 ? 123456789 n = 0？ 10 ? ∞ n Pythagorean theorem: x+y = z has a nonzero positive integer solution: 2 2 3,4,5; 5, 12, 13. Its general solution is: L x = a? B, y = 2ab, z = a+b 2 3 2 where a > B is an odd or even integer. So, does the cubic indefinite equation: x+y = z have a nonzero positive integer solution? 3 this is the famous Fermat conjecture: x+y = z n n n n n n n when n > 2, there is no positive integer solution! Fermat wrote on the edge of a book that he has solved this problem, but it will remain a suspense for the next 300 years. /kloc-Euler, the greatest mathematician in the 8th century, proved that Fermat's Last Theorem holds when n = 3,4. It turned out that when n