- 3021 - MATH - a learned discipline? - Mathematics is so amazing because it recreates and communicates so much of nature in its language and logic. A simple “pi” can represent all the perfect circles in the Universe. Their circumference is always 3.14 times larger than their diameter.
-------------- 3021 - MATH - a learned discipline?
- It is one of the laws of mathematics that “pi” is an irrational number that can not be formed as a fraction and as a decimal the numbers continue to infinity, never repeating, pi = 3.14176254254.…… etc
Yes, this is very irrational.
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- Pythagoras (572-497 B.C.) introduced the term “ mathematics”. He called it a learned discipline. From that moment it has been controversial as to whether the discipline invents or discovers the laws of mathematics, the laws of Nature.
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- Here are some discoveries. Take 365 days in a year. You can get the number 365 by taking the sum of the squares of 10, 11, and 12.
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--------------- 10^2 + 11^2 + 12^2 = 100 + 121 + 144 = 365
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- Or, you can get the number 365 by taking the sum of the squares of 13 and 14.
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--------------- 13^2 + 14^2 = 169 + 196 = 365
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- How about the number 100. You can get that number by summing the cubes of the first four numbers, 1 ,2, 3, and 4.
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--------------- 1^3 + 2^3 + 3^3 + 4^3 = 1 + 8 + 27 + 64 = 100
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- Then someone discovered that the sum of odd consecutive numbers always equals a number squared:
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--------------- 1 = 1^2
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--------------- 1 + 3 = 2^2
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--------------- 1+3+5 = 3^2
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--------------- 1 + 3 + 5 + 7 = 4^2
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--------------- 1 + 3 + 5 + 7 + 9 = 5^2
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----------------- etc. …………….
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----------------- Why is that?
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- Of course Pythagoras discovered that the square of the hypotenuse is always and everywhere equal to the sum of the squares of the other two sides.
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---------------- c^2 = a^2 + b^2
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- But, also the discover was made that for any triangle, not just a right triangle, with the angles A, B, C and sides opposite a, b, c respectively.
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-------------- a^2 = b^2 + c^2 - 2bc cosA
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- The square of the side opposite the cosine angle is equal to the sum of the squares of the other two sides minus 2 times the product of these two sides and the cosine of the angle between them. Another law of mathematics.
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- The area of a triangle is ½ the base times the height. A = ½ b*h
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- But, the area of any triangle is A = ½ a*b sinC
- This ideas of areas bets even stranger for polygons. The area of a polygon is equal to the number of points (vertices) plus ½ the number of boundary edges minus 1
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------------- A = i + b/2 - 1
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- “Epistemology” is the investigation into the limits of human knowledge. How far can mathematics take us into our understanding of the Universe?
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- Every even integer greater than 2 is the sum of 2 prime numbers:
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-------------- 4 = 2 + 2
--------------- 6 = 3 + 3
---------------- 8 = 3 + 5
--------------- 10 = 3 + 7
---------------- 12 = 5 + 7
--------------- 14 = 3 + 11
---------------- 16 = 5 + 11
--------------- etc. ………………..
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---------------- Why is that ?
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- Books have been written on each of these numbers, pi, “e” the natural logarithm , the golden ratio 1.618 See the footnote for some of the book reviews.
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-------------- the Golden Ratio = (1 + 5^12) / 2 = 1.618 …….
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- The Golden Ratio is the sum of 2 n umbers divided by the larger number:
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--------------- (a + b) / b = 1.618
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---------------- (21 + 34 ) / 34 = 55 / 34 = 1.617
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---------------- 10,946 + 6,675 ) / 10,946 = 17,711 / 10,946 = 1.618
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- “e” the natural logarithm is in the most famous mathematical equation:
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---------------- e ^i*pi + 1 = 0
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- The natural logarithm raised to the imaginary “pi” is equal to -1. You can explore the limits of mathematical knowledge, it goes on forever:
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----------------------------- Other reviews available:
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(1) #1086 “ Formulas for space, time and velocity “
(2) #1087 “ Formulas for space, time and velocity “
(3) #1088 “ Formulas for space, time and velocity “
(4) #1089 “ Formulas for space, time and velocity “
(5) #1090 “ Formulas for space, time and velocity “
(6) #1042 “ Calculating areas by counting dots“
(7) #1041 “ The star with the golden ratio “
(8) #745 “ The calculus of a circle “
(9) #853 “ Math, the golden ratio “
(10) #803 “ Transcendental numbers “e” and “pi” “
(11) #649 “ The Greeks invented numbers “
(12) #805 “ Gambling “
(13) #796 “ Science and math “
(14) #798 “ Science and math, Part II “
(15) #799 “ Science and math , Part III“
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February 4, 2021 MATH - a learned discipline? 1095 3021
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--------------------- --- Friday, February 5, 2021 ---------------------------
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