Stellar Numbers. In this study, we analyze geometrical shapes, which lead to special numbers. We consider various geometrical patterns of evenly spaced dots and derive general statements of the nth special numbers in terms of n.

The first 200 words of this essay...

Timur Karimov

Anglo - American School of Moscow

IB Mathematics

Internal Assessment Portfolio Practice 1

Aim: The aim in this task is to consider geometric shapes, which lead to special numbers. The simplest examples of these are square numbers, 1, 4, 9, and 16, which can be represented by squares of side 1, 2, 3 and 4.

Introduction: In this study, we analyze geometrical shapes, which lead to special numbers. We consider various geometrical patterns of evenly spaced dots and derive general statements of the nth special numbers in terms of n. Henceforth, all tables and mathematical formulas are generated by the Microsoft Word. All the stellar and triangular number visual representations are modulated using GeoGebra 4. The rest of the shapes are generated by "insert shape" function of Microsoft Word.

Task 1

The first task is to complete the triangular numbers sequence with three more terms.

As we can see, each successive triangle pattern numbered (n is the stage number) can be derived from the previous one number () by simply adding evenly spaced dots on either of the sides of the triangle.

In other words, the number of dots in