Ilumin8

Digit Sum Spiral

Task 1:

Digit-sum spiral for multiples of 3:

  1. Write out multiples of 3 in a column ( up to 15 x 3?) Write the digit-sum alongside each number. (3,6,9,3,6,9,3,6,9,3......)
  2. Discuss any patterns that can be seen in the sequence of digit sums.
  3. Start to draw the spiral (0.25 cm squared paper is recommended) :
  4. Starting point is at the top of the page, in the centre.
  5. First line : RIGHT 3 squares
  6. Turn clockwise 90 degrees, then DOWN 6 squares
  7. Turn clockwise 90 degrees, then LEFT 9 squares.....
  8. Turn clockwise 90 degrees, then UP 3 squares...
  9. Continue turning and using the digit sums until the starting point is reached: the 'spiral' is now complete!

It is perfectly OK to draw over part of a line that has already been drawn.

Task 2

This activity is an exploration of the images that result when digit-sums are found for the multiples of a given number, and then a “spiral” is drawn on a squared grid with the lengths of the lines determined by the numbers obtained as the digit-sums (Figure 1).

Firstly, what is a digit-sum? Using 149 as an example: 1 + 4 + 9 = 14 and 1 + 4 = 5, so the digit sum of 149 is 5.

To create a digit-sum spiral for multiples of 7:

  1. Find the digit-sums for the first 20 or so multiples of 7.
  2. Notice that there is a pattern in the sequence of digit sums.
  3. Start to draw the spiral (0.25 cm squared paper is recommended).
  4. Starting point is at the left hand side of the paper, half way up.
  5. Draw the first line: UP 7 squares.
  6. Turn clockwise 90 degrees, then RIGHT 5 squares …
  7. Turn clockwise 90 degrees, then DOWN 3 squares ...
  8. Turn clockwise 90 degrees, then LEFT 1 square ...
  9. Continue turning and using the digit sums until the starting point is reached: the 'spiral’ is complete (Figure 2).

Figure 2

Digit-sum spiral for multiples of 7

Figure 1

Digit-sum spiral for multiples of 3