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What is Parkside's Triangle?

Derek Schauland
Derek Schauland

Parkside's Triangle is a mathematical pattern that generates a triangle of numbers given two variables, the size and the seed. The size variable, N, must meet the following condition: 1 <= N <= 20. This means that N can be any number greater than or equal to 1 and any number less than or equal to 20. N must therefore be between 1 and 20 inclusive.

The number N represents the rows of the triangle. If N = 5, then there are 5 rows making up the triangle. The first row of the triangle can have no blank number within it. All positions must contain a number greater than or equal to 1. The other variable is the seed, S, which represents the first number in the first row of the triangle. The seed must meet the following conditions: 1 <= S <= 9. The seed must be greater than or equal to 1 and less than or equal to 9.

When the size and seed variables are known, this particular pattern is produced. An example would look like this:

Size = 4 Seed = 1

1 2 4 7
3 5 8
6 9

Size = 5 Seed = 3

3 4 6 9 4

5 7 1 5
8 2 6
3 7
Scientist with beakers
Scientist with beakers

The pattern of numbers to create the triangle counts beginning at the left of the bottom row and then moves right and down. Each time the next row is added, all the numbers count from the first row downward. In both directions, Parkside's Triangle will contain the same number of rows.

Many computer programming classes in languages such as C use an example program to create this pattern for any given size and seed. The program will read in the size and the seed and output the correct pattern of numbers. This is accomplished using loop logic and basic arithmetic along with programming skills and can be used to present the fundamentals of loop logic.

Other than the specified size and seed conditions to begin creating the pattern, there are no other limits to Parkside's Triangle. In any iteration, it will have no more than 20 rows and a beginning number no higher than 9. As shown in the example triangle above, there are also no zeroes.

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      Scientist with beakers