Page 15 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\01_Chapter_1\Chapter_1
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

(d) Tetrahedral Numbers: The numbers that can be represented by the layers of triangles forming
a tetrahedron shape are called tetrahedral numbers. Example: 1, 4, 10, 20, ...

1 4 10 20
(e) Pentagonal Numbers: Pentagonal numbers are the numbers that can be represented in the
shape of a pentagon. Unlike other figurative numbers, the vertices remain the same while
the layers increases. Example : 1, 5, 12, 22, 35, ...

1 5 12 22 35
(f) Hexagonal Numbers: When dots are arranged in such a way that they form a hexagon, the
numbers are termed as hexagonal number. Example: 1, 6 ,15, 28, ...
Here also, the vertices remain the same while the layers increases.

1 6 15 28
Hexagonal numbers and centred hexagonal numbers are different.
In the centred hexagonal number pattern, the previous number is placed at centre and another
layer is created around. Example: 1, 7, 19, 37, ...

1 7 19 37

Think and Answer
Remember
Are there centred pentagonal numbers?
If yes, find the first five such numbers and make A number which can be shown visually by a plane
dots patterns for them. geometrical shape is called polygonal numbers.

13 Patterns in Mathematics