Ilumin8
Digit Sum Spiral
Task 1:
Digit-sum spiral for multiples of 3:
- 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......)
- Discuss any patterns that can be seen in the sequence of digit sums.
- Start to draw the spiral (0.25 cm squared paper is recommended) :
- Starting point is at the top of the page, in the centre.
- First line : RIGHT 3 squares
- Turn clockwise 90 degrees, then DOWN 6 squares
- Turn clockwise 90 degrees, then LEFT 9 squares.....
- Turn clockwise 90 degrees, then UP 3 squares...
- 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:
- Find the digit-sums for the first 20 or so multiples of 7.
- Notice that there is a pattern in the sequence of digit sums.
- Start to draw the spiral (0.25 cm squared paper is recommended).
- Starting point is at the left hand side of the paper, half way up.
- Draw the first line: UP 7 squares.
- Turn clockwise 90 degrees, then RIGHT 5 squares …
- Turn clockwise 90 degrees, then DOWN 3 squares ...
- Turn clockwise 90 degrees, then LEFT 1 square ...
- 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
Links and other activities
Figure 1
Digit-sum spiral for multiples of 3