Summary
(1) Mathematics may be viewed as the search for patterns and for the explanations as to why those patterns exist.
(2) Among the most basic patterns that occur in mathematics are number sequences.
(3) Some important examples of number sequences include the counting numbers , odd numbers, even numbers, square numbers, triangular numbers, cube numbers, Virahānka numbers, and powers of 2.
(4) Sometimes number sequences can be related to each other in beautiful and remarkable ways. For example, adding up the sequence of odd numbers starting with 1 gives
(5) Visualising number sequences using pictures can help to understand sequences and the relationships between them.
(6) Shape sequences are another basic type of pattern in mathematics. Some important examples of shape sequences include regular polygons, complete graphs, stacked triangles and squares, and Koch snowflake iterations. Shape sequences also exhibit many interesting relationships with number sequences.