JANUARY 10, 2024
10th day of Year 2024 ( a leap year).
1. Hindu Number System contains 10 digits (0 - 9).
2. Pythagoreans loved the number 10 as it is perfectly associated with music. It can be symbolized by the Tetractys. The tetractys is a triangular figure consisting of 10 dots arranged in 4 rows.
The first row represented zero (0) dimensions --- A point
The second row represented one dimension ---- A line is connected by two points.
The third row represented two dimensions. --- A triangle connected by three points.
The fourth row represented three dimensions --- A tetrahedron defined by four points.
The Pythagorean musical system was based on it as the ratios of 4 : 3 , 3 : 2 and 2 : 1 forms the basic intervals of the Pythagorean scale.
3. Here is a mathematical puzzle:- Suppose you have a 10 x 10 square container containing 100 balls arranged as shown below --
Can you insert 5 more balls in the same container, making the count 105?
Here is a solution. Just try it.
The arrangement of balls made the basic difference.
4. This interesting formula came in Srinivasa Ramanujan's dream.
5. Powers of 10 contain divisors, where is the number of digits.
10 has 22 = 4 divisors ( 1, 2, 5 and 10)
100 has 32 = 9 divisors ( 1, 2, 4, 5, 10, 20 25, 50 and100)
1000 has 42 = 16 divisors ( 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100,
125, 200, 250, 500, and 1000)
5. It is the fourth triangular number. The first three are 1, 3 and 6.
6. It is the sum of square of two consecutive odd numbers.
10 = 12 + 32
7. Take any triangle and divide each side into three equal parts. Draw lines from these to the opposite corners. A new shape will appear in the middle of the triangle whose area is 1/10th of the area of whole triangle. This is known as Marion Walter Theorem. This theorem state - the area of the central hexagonal region determined by trisection of each side of a triangle and connecting the corresponding points with the opposite vertex is given by 1/10 the area of the original triangle.
8. The only known solution to
n! = a! b! is 10! = 6! X 7!
9. There are only 11 powers of 10 that are products of two integers without any zero. These are-- 100 = 1 101 = 2 x 5 102 = 4 x 25
103 = 8 x 125 104 = 16 x 625 105 = 32 x 3125 106 = 64 x 15625 107 = 128 x 78125 109 = 512 x 1953125
10. It is the first number whose fourth power ( 10 x 10 x 10 x 10 = 10000) can be written as a sum of two squares in two different ways
10000 =
=
11. A math lover K Srinivas Raghava has defined 10 using the Golden number as ---
Mathematicians born/died on 10th January
Born:
- 1875: Issai Schur
- 1899: Szolem Mandelbrojt
- 1905: Ruth Moufang
- 1906: Rafael Laguardia
- 1906: Grigore Moisil
- 1922: Douglas Jones
- 1938: Donald Knuth
Died:
- 1833: Adrien-Marie Legendre
- 1843: Louis Puissant
- 1929: Karl Heun
- 1941: Issai Schur
- 1944: Thomas Scott Fiske
- 1976: Alexander Buchan
- 1984: Stephen Bosanquet
- 1998: Wolfgang Hahn
- 2014: David Cariolaro
Interesting Events of Day (10th January)
1. On 10th January 1844, George Boole submitted his first mathematical paper in Royal Society which was rejected as the author of the paper was unknown. Later, it was reviewed by two referees and interestingly, one referee rejected the paper whereas the other recommended it for award. This paper became the first paper to receive the GOLD medal from the Royal Society.
2. On 10th January 1854, Riemann while presenting a paper at Gottingen challenged the mathematical world to redefine the concept of infinity which should either be endless or unbounded.
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1 comment:
This is a quick revision of the class 👍👍
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