Number Multiplier Pattern Generator
Generates a visual pattern to illustrate properties of multipliers in different number bases.
What is being generated by this program?
The number 9, when multiplied by any number, has digits which when added together repeatedly until only one digit remains, always add to 9. In the same way, other numbers display patterns when they are multiplied repeatedly by the same number and then condensed through addition.
For instance when the numbers 3 or 6 are doubled, they always add to either 3 or 6. 3 doubles to become 6, 6 doubles to become 12 (1+2 = 3), 12 doubled becomes 24 (2+4 = 6) and so on.
Other numbers when doubled, then condensed, follow the pattern of 1-2-4-8-7-5, and the reverse order when divided by two. For instance 1 doubles to become 2, 2 doubles to become 4, 4 doubles to become 8, 8 doubles to become 16 (6+1 = 7), 16 doubles to become 32 (3+2 = 5), 32 doubles to become 64 (6+4 = 10, 1+0 = 1) and so on. Similarly 1 divided by 2 becomes 0.5 (0+5 = 5), 0.5 divided by 2 becomes 0.25 (0+2+5 = 7) and so on.
The number 9, when multiplied by any number, has digits which when added together repeatedly until only one digit remains, always add to 9. In the same way, other numbers display patterns when they are multiplied repeatedly by the same number and then condensed through addition.
For instance when the numbers 3 or 6 are doubled, they always add to either 3 or 6. 3 doubles to become 6, 6 doubles to become 12 (1+2 = 3), 12 doubled becomes 24 (2+4 = 6) and so on.
Other numbers when doubled, then condensed, follow the pattern of 1-2-4-8-7-5, and the reverse order when divided by two. For instance 1 doubles to become 2, 2 doubles to become 4, 4 doubles to become 8, 8 doubles to become 16 (6+1 = 7), 16 doubles to become 32 (3+2 = 5), 32 doubles to become 64 (6+4 = 10, 1+0 = 1) and so on. Similarly 1 divided by 2 becomes 0.5 (0+5 = 5), 0.5 divided by 2 becomes 0.25 (0+2+5 = 7) and so on.
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When the numbers 1-9 are placed around a circle this pattern of repetition can be represented like this.
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This program allows these patterns to be displayed for different number bases and multiplier values.
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