# Stellar numbers portfolio

STELLAR NUMBERS                                                                                                       SL TYPE I

Introduction: In this following assignment, I will be considering geometric shapes that lead to special numbers. The simplest examples of these are square numbers (1, 4, 9, 16, etc), which are derived from squaring 1, 2, 3, and 4. From this I got the equation y= x2. This equation is illustrated in the table below.

y=x2

In the table on the left, I observe that from the y value 1 to the y value 4 there is an increase of 3. From the y values 4 to 9, there is an increase of 5. From the y values 9 to 16, there is an increase of 7. This shows that it goes: +3, +5, +7, which is then increasing by 2 between each of those numbers.

Below, is the graph of y=x2

The equation y=x2 comes from the general equation y= ax2-bx+c.

Y=x2 is the same as y=x2+0x+0. Therefore, a=1, b=0, and c=0.

The next example I am going to show you is similar to the one above. The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular numbers (1, 3, 6, 10, 15, 21, 28, 36).

In the table on the left, I observe that from the y value 1 to the y value 3 there is an increase of 2. From the y values 3 to 6, there is an increase of 3. From the y values 6 to 10, there is an increase of 4. This shows that it goes: +2, +3, +4, which is then increasing by 1 between each of those numbers.

This follows the form of an arithmetic sequence, because each new term is equal to the sum of the previous term plus the term number. A formula for ...