# Making the Perfect Heart

Ian's constructive geometry method for the perfect heart. I assume everyone remembers how to draw a perfect square using just compasses and a straight edge, right? I imagine there is an age gap there!

We make Valentine’s cards for one another here. This year I went out on a quest for the perfect heart-shape. A good blend between proportion, curve, and size. The best I discovered was very simple. Take a square, and use two adjacent sides as the diameters of circles. The result, when rotated by 45 degrees, is a darn fine heart shape, though I say it myself.

And the best bit of all is it is really easy to program, when you want to create a card with ten thousand hearts on it, for example đŸ™‚

What I think is a minimal greek (compass and straight edge) construction of my heart shape. If you can do it in fewer marks, I'd be interested to know. If you can't see the animation, click to put it on its own page.

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### 7 responses to “Making the Perfect Heart”

1. A perfect heart, indeed! And crafted from the stuff of our existence . . .

2. So, for purists, the next Euclidean puzzle: Using only a compass and a straight edge, how does one bisect the squares to adjacent sides to find the center point to anchor the compass for the circles.

Here is the answer: “For you Patriots” — must be for home schoolers.

3. Ian

Eugh, my technical drawing teacher would have freaked to see that. For a start she uses blobs for end points (where in the blob, exactly, is the end?), second she pushes on the compasses while drawing the arcs, thus changing their size. Might as well just eyeball it.

Oh, and you only need to bisect one edge, because that bisection allows you to draw both curves. I’ll attach a wee animation to the main post.

4. Nr

My version. I think it’s simple. Uses 5 lines and 9 circles.

5. Ian

It is simple, but it doesn’t construct as nicely as your sketch. The lobes of the heart don’t meet at the center line, not if they are tangent to the horizontal and vertical, and centered at the intersection between the large circle and the diagonal blue bisector. One of those situations where doing a greek construction with fat pens makes things look like they work.