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Brain Sizzlers

Draw as many lines as possible by joining any two dots in the following cases. Write the numbers of
line segment in the sequence and explain it.

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MAths connect

The images given above show natural patterns. Fibonacci numbers are evident in nature, e.g., pineapples, sunflowers,
etc. In a pineapple, the spirals are 8, 13 and 21. Clockwise and anticlockwise spirals in a sunflower are 34 and 55
or 55 and 89 up to 144.
Some flowers and fruits have Fibonacci sequence/Virahanka numbers in them. Name some flowers that have
1, 2, 3, 5, 8, 13, 21, 34, ..... petals. You can also find the spirals in different fruits that follow the Virahanka sequence.

Mental Maths
1. Name the number sequence given here: 2, 4, 6, 8, 10, 12, 14, ...
2. What will come next in the given number sequence? 1, 8, 27, 64, 125, 216, ...
3. What type of number is 19 – a triangular or hexagonal number? Make a dot pattern to support your answer.
4. Can you think of pictorial ways to visualise the sequence of tetrahedral numbers?
5. Think of a pictorial explanation for why adding counting numbers up and down, i.e., 1, 1 + 2 + 1, 1 + 2 + 3 +
2 + 1, …, gives square numbers.

maths fun
The Fibonacci sequence is the series of numbers where each number is the sum of the two
preceding numbers. For example: 1, 1, 2, 3, 5, 8, 13, 21, 34, …
Take the help of the internet to explore about the Fibonacci spiral. Fill the Fibonacci numbers in the given
Fibonacci spiral. Also make it colourful.

21 Patterns in Mathematics