ON BEAUTY IN MATHEMATICS

1. Is Beauty a mathematical concept?2. Can mathematical structures

look beautiful? What properties lend beauty to mathematical structures

3. What mathematical components lend beauty to a visual structure?

The math within the genes

Roman Broccoli

Spiral: The shape of a galaxy

Bubbles – Fractals and self-referential structures can generate this

Generated by Fractals

Humourous? but True!

Is Beauty a mathematical concept?

Symmetry

Proportion

Progression

Colours: Variety, Combination, Melding

Arithmetical Curiosities

123456789 x 8 + 9 = 987654321

123456789 x 9 + 10 = 1111111111

111111111 x 111111111 = 12345678987654321

Patterns and Symmetry in Numbers 12345679 x 9 = 111111111 12345679 x 18 = 222222222 12345679 x 27 = 333333333 12345679 x 36 = 444444444 12345679 x 45 = 555555555 12345679 x 54 = 666666666 12345679 x 63 = 777777777 12345679 x 72 = 888888888 12345679 x 81 = 999999999

Note the missing 8 in the base number

Number Patterns Galore! 1 x 8 + 1 = 9 12 x 8 + 2 = 98 123 x 8 + 3 = 987 1234 x 8 + 4 = 9876 12345 x 8 + 5 = 98765 123456 x 8 + 6 = 987654 1234567 x 8 + 7 = 9876543 12345678 x 8 + 8 = 98765432 123456789 x 8 + 9 = 987654321

Yet another Pattern 1 x 9 + 2 = 11 12 x 9 + 3 = 111 123 x 9 + 4 = 1111 1234 x 9 + 5 = 11111 12345 x 9 + 6 = 111111 123456 x 9 + 7 = 1111111 1234567 x 9 + 8 = 11111111 12345678 x 9 + 9 = 111111111 123456789 x 9 +10= 1111111111

Look at this Pattern 0 x 9 + 8 = 8 9 x 9 + 7 = 88 98 x 9 + 6 = 888 987 x 9 + 5 = 8888 9876 x 9 + 4 = 88888 98765 x 9 + 3 = 888888 987654 x 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888

Beauty of 7 72 = 49 672 = 4489 6672 = 444889 66672 = 44448889 666672 = 4444488889 6666672 = 444444888889 66666672 = 44444448888889

Properties of Number Systems If 1 is added to the product of two

consecutive odd numbers, the result will be square of the even number between the odd numbers.

Properties of Number Systems If 1 is added to the product of two

consecutive odd numbers, the result will be square of the even number between the odd numbers.

E.g. Let the two numbers be 17 and 19.17 x 19 = 323Add 1 => 324182 = 324.

Properties of Number Systems If 1 is added to the product of two

consecutive even numbers, the result will be square of the odd number between the even numbers.

E.g. Let the two numbers be 12 and 14.12 x 14 = 168Add 1 => 169132 = 169.

Properties of Number Systems (contd)

The square of any odd number (other than 1) can be expressed as sum of two consecutive natural numbers.

Check it out!

Properties of Number Systems (contd)

Cubes of numbers ending with digits 1, 4, 5, 6 and 9 will also end with same digit (1, 4, 5, 6 and 9).

Properties of Number Systems (contd) Cubes of numbers ending with digits 1,

4, 5, 6 and 9 will also end with same digit (1, 4, 5, 6 and 9).

Cubes of numbers ending with digits 2 will end with 8 while cubes of numbers ending with digits 8 will end with 2. Similarly cubes of numbers ending with digits 3 will end with 7 while cubes of numbers ending with digits 7 will end with 3.

The Words of Numbers The person who generated this sentence must

be a vocabulary GENIUS. Read the sentence below carefully...

"I do not know where family doctors acquired illegibly perplexing handwriting nevertheless, extraordinary pharmaceutical intellectuality counterbalancing indecipherability, transcendentalizes intercommunications incomprehensibleness".

In this sentence the Nth word is N letters long. e.g. 3rd word is 3 letters long...

Math / Non-math “It is impossible to be a mathematician without

being a poet within the soul” – Sofia Kovalevskaya

“All considerations of the mind-brain, including qualitative, artistic, literary, poetic or musical, tactile sensations … are representations as neural signals, which are basically mathematical representations” – Anonymous

A Poser to end The image within the mirror experiences

left-right inversion, i.e. left becomes right, and right becomes left. Right?

Well, why is there no top-bottom inversion?

Acknowledgement Besides the Internet sources,

I am grateful for the compilation given me by PB M V Rao (Hyderabad).

PB M V Rao (formerly of L&T) releases a regular column “Beyond Maths” which seems best suited for youngsters, with a mix of math, language, wisdom and jokes…

Check it out. Contact rao_m_v@yahoo.com.

Thank You !!