Practice measuring skills by drawing this Valentine's Day heart

Martin Hansen

I hope that the above banner caught your eye. It was intended to do so, as I designed it as a rear window sticker for my car. A larger version is proubly on display in my classroom and, come next St Valentine's day, I am all set to woo the woman of my dreams! It is clearly a design with possibilities and, certainly, what teacher could fail to be impressed if something similar were to adorn a mathematics exercise book? So, if you are after a good report this term, here is how to begin.
 
From a Geometry Set you need (i) a pencil, (ii) a ruler, and (iii) a protractor.
(A)  On an A4 size sheet of plain paper place a dot, roughly in the centre.
(B)  Place the protractor's “centre” over the centre dot.
(C)  Lightly mark 18 “circumference” dots around the protractor, the spacing between each dot being 20° of angle. See Figure 1.

(D)  Use the ruler to lightly draw a “spoke” between a “circumference” dot and the centre dot.
(E)  Repeat for each “circumference” dot. See Figure 2.
(F)  Measure 1 cm from the centre dot along one “spoke” and make a mark.
(G)  Measure 2 cm from the centre dot along the “spokes” to the left and right of the starting “spoke” and make marks. Join these marks to that on the starting “spoke”.
(H)  Continue clockwise and anticlockwise, measuring first 3 cm, then 4 cm, then 5 cm and so on until the lines meet 10 cm out along the final “spoke”. See Figure 3.
(I)  Use two colours in alternation to finish off the mathematical love heart.

Variations in the areas shaded and of the borders surrounding the heart are illustrated in the diagrams. Use your imagination and enjoy making your own alterations and, indeed, find out that other mathematical “pictures” are possible using the same basic idea of Archimedes' spiral.

Plus, Autumn 1991, Number 19
© The Mathematical Association. ISSN 0268-2095
Article reset for MathMagical website, February 2012

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