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November 10, 2019

What are some mind-blowing facts about mathematics?

Mathematics is itself mind blowing. It is not only a subject or a topic but it is the description of life. Nothing is possible without Mathematics. Mathematics is not only about interest but it is about excellence. People often misguide the subject as “full of problems” but without problems is there any solution?

Lets begin with the definition of Mathematics. It can be stated as a subject including topics on algebra, geometry,number theory,arithmetic,analysis,geometry and many more. But in reality there is no definition of Mathematics. This is such a path which can be traveled only if you start visualizing its properties. It is all about measurement,counting,conjectures,analyzing,numbers,calculation and most importantly logic.

Now coming to the question some of the mind blowing facts about Mathematics

  • Invention of ZERO, one of the most important discoveries till date is zero and zero is actually an even number.
  • Hundred is derived from the word “Hundrath” which in Old Norse meant 120 meaning Long Hundred.
  • There are a number of prime numbers but 2 is the only ‘even’ prime number.
  • There is no Roman numeral representation of Zero where as all oher numbers can be written in Roman Numerals.
  • 4 is the only number spelled with the numbers of letters equal to its value.
  • Aryabhatta did not provide any symbol to Zero. The symbol of Zero was used in an Arithmetic manual of merchants, Bakhshali Manuscript.
  • The Fibonacci sequence invented by Leonardo Fibonacci has practical applications in nature. Breeding of Rabbit follows the Fibonacci sequence. The sequence is given as 0,1,1,2,3,5..... where each term is the sum of preceding terms.The spiraling pattern of the sunflower and Pinecones follows the Fibonacci sequence.The branches of tree are also arranged in Fibonacci sequence. Even the galaxies follows Fibonacci pattern.
  • 10! seconds = 6 weeks.

Lets check the above fact if its true or not

Value of 10! = \(1*2*3*4*5*6*7*8*9*10\) = 3,628,800 seconds

Now converting to minutes we get \(\frac{3628800}{60}\)= 60,480 minutes( 1 minute = 60 seconds)

Converting to hours \(\frac{60480}{60}\) = 1,008 hours (1 hour= 60 minutes)

Converting to days \(\frac{1008}{24}\) = 42 days (1 day= 24 hours)

6 weeks =\( 6*7\)= 42 days ( 1 week = 7 days)

Now the number 11711 is a Palindrome number, that is numbers that read the same from forwards and backwards.

  • First Electronic Calculator was created in 1960s.
  • A 100-sided polygon is called a hectogon OR centagon.
  • Two numbers are said to be in Golden ratio if they are in the ratio of the sum of the numbers to the larger number. Most of the things in nature occurs according to this ratio including the spiral arrangement of leaves . The value of Golden ratio 1.618.
  • Fibonacci Sequence and Golden ratio are interlinked
  • The Fibonacci sequence is 0,1,1,2,3,5,8,13,21,34,55.........

Now going by the golden ratio dividing each number by previous number we get \(\frac{1}{1}\)=1 , \(\frac{2}{1}\)=2 , \(\frac{3}{2}\)=1.5 , \(\frac{5}{3}\)= 1.6666, \(\frac{8}{5}\)= 1.6, \(\frac{13}{8}\) = 1.625 , \(\frac{21}{13}\)= 1.61 , \(\frac{34}{21}\)=1.619 , \(\frac{55}{34}\)=1.617

We notice the values are converging towards 1.618 which is the golden ratio.

  • The number 5040 has unique properties that is , this number is the sum of 42 primes that is 42 consecutive primes and that is 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 +163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229.
  • The number 3 has various properties like

It is the first prime number which is odd.

It is a factorial prime number .A factorial prime is a prime number which is one less pr more than a factorial

3 is a factorial prime because 3!= (2!+1) = 6

It is a Mersenne prime number too.Now in mathematics Mersenne prime number is a prime number which is 1 less than a power of 2 that is

\(2^n\) - 1 , where n is an integer.

3 can be written as 3= \(2^2\) - 1 = 4-1

Now MATHEMATICS can be divided into two parts-

  1. Pure Mathematics
  2. Applied Mathematics

Pure Mathematics is devoid of any applications outside Mathematics. Its solely pure containing deeper aspects and a vivid study on Mathematics.The results obtained from pure Maths are greatly useful for practical applications.Concept of pure Mathematics was obtained around the year 1900.Most of the Mathematical theories are obtained from real world and less from the applied world.

Topics under Pure Mathematics includes

  1. Algebra( factorization, Group theory, Ring Fields, Metric space,Gaussian space, Theory of Equations,Binary Operations)
  2. Calculus( limits,continuity, differentiation, integration, relations and functions)
  3. One of the best of Mathematics Number Theory( Fermat’s Theorem, Mean value Theorem, Euler’s theorem phi function, Lagrange’s Theorem, Integers, Real Numbers, Complex Numbers, Rational and Irrational Numbers, Quadratic Equations, Cardan;s Method, Ferrari’s Method, Mathematical Induction, Polynomials,Topology,Real and Complex Analysis).
  4. Logic( set theory,cardinal,Boolean Algebra)
  5. Combinatorics
  6. Geometry (Planes,Straight Lines,Curves, Polynomials,Construction, angles)

Applied Mathematics is the application of Mathematical topics in various fields like Engineering, Business, Industry, Computer Science. The term “Applied” means applying Mathematics in professional fields by studying Mathematical models.

Topics under Applied Mathematics include

  1. Differential Equations , a Mathematical Equation containing unknown functions and derivatives. It is mostly comprised of Calculus. There are two types of differential equations- Ordinary Differential Equation (contains one or more functions of one independent variable and derivative of those functions) and Partial Differential Equations (involves derivatives in multiple variables).
  2. Mathematical Physics ( Quantum Theory, Wave Theory, Ray optics etc)
  3. Statistics and Probability.

Well, going into a deeper thought not all of the things around us revolves around Mathematics?

Lets consider our daily routine , Marketing and shopping without numbers or basic Arithmetic is shopping possible?No then what are numbers and money all about? Mathematics. Reaching a place within time let it be school or any other work place, what is time about? Hours seconds and minutes!! Again Mathematics. Speed Distance and time dont we apply it in daily life? This is also Mathematics. Profit and Loss, Sales Tax, Value Added Tax everything is about Mathematics. Thus Mathematics is not just a subject but it is a visualisation of our daily life.

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