MATHS IN

NATURE &

MATHS MARVELS

INTRODUCTIONNature is surrounding us, mathematics is around us – in every flower we see…, in every beauty of nature, we can see the glimpse of mathematics.Mathematics is the way of explaining the chaotic world around us with a magic of numbers.

SHAPES-CONES

Volcanoes form cones, the steepness and height of which depends on the runniness (viscosity) of the lava. Fast, runny lava forms flatter cones; thick, viscous lava forms steep-sided cones. Cones are 3-dimensional solids whose volume can be calculated by

1/3 x area of base x height.

Shapes - Polyhedron

For a beehive, close packing is important to maximize the use of space. Hexagons fit most closely together without any gaps; so hexagonal wax cells are what bees create to store their eggs and larvae. Hexagons are six-sided polygons, closed, 2-dimensional, many-sided figures with straight edges.

SHAPES - PERFECT

Earth is the perfect shape for minimizing the pull of gravity on its outer edges - a sphere (although centrifugal force from its spin actually makes it an oblate spheroid, flattened at top and bottom). Geometry is the branch of maths that describes such shapes.

Golden ratio (phi)

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The ratio of consecutive numbers in the Fibonacci sequence approaches a number known as the golden ratio, or phi (=1.618033989...). The aesthetically appealing ratio is found in much human architecture and plant life. A golden spiral formed in a manner similar to the Fibonacci spiral can be found by tracing the seeds of a sunflower from the centre outwards.

FIBONACCI SERIESIn 1202, LEONARDO

FIBONACCI discovered a numerical series known as Fibonacci Series.

It is a simple series but its applications are limitless.

It has of a lot of endless examples.

PROCEDURE

Starting with 0 and 1, each new number in the series is the sum of the two numbers before it.0,1,1,2,3,5,8,13,21,34,55,89,144…Here, f₁=0, f₂=1, f₃=f₁ + f₂ =0 + 1 =1

The series continues like this.

1. FIBONACCI SPIRALFibonacci spiral is an example of Fibonacci series.

2.FLOWERS

In flowers, number of petals give a Fibonacci sequence.

3. PINEAPPLES

In pineapples, seed heads gives Fibonacci sequence.

An Armstrong number or a plus perfect number is a number that is the sum of its own digits each raised to power of it’s digit.

General formabc = aⁿ + bⁿ + cⁿ

EXAMPLES

153 = 1 + 5 + 3370 = 3 + 7+ 0371 = 3 + 7+ 1

A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷) and sometimes exponentiation.

EXAMPLES

347 = 73 + 4 25 = 5 1024 = (4 − 2)10 001729 = 1700 + 29.

A Dudeney number is a positive integer that is a perfect cube such that the sum of its decimal digits is equal to the cube root of the number.

EXAMPLES 512 = 8 x 8 x 8 ; 8 = 5 + 1 + 2 4913 = 17 x 17 x 17 ; 17 = 4 + 9 + 1 + 3 5832 = 18 x 18 x 18 ; 18 = 5 + 8 + 3 + 217576 = 26 x 26 x 26 ; 26 = 1 + 7 + 5 + 7 + 619683 = 27 x 27 x 27 ; 27 = 1 + 9 + 6 + 8 + 3

BY: MAHIMA KAPOOR NEHA GUPTA SHAILAJA CHAUHAN