![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
Prime Cake
Jan. 30th, 2008 08:38 amSunday was my husband's birthday, so I baked him a heart-shaped cake. It's something my mom used to make for me because my birthday is near Valentine's Day (she got the idea out of a magazine, she tells me). Basically, you bake two layers of cake, one in a square pan and one in a round pan with the same diameter as the side of the square. Then, instead of layering them vertically, you slice the circle in half, turn the square diamond-wise and plunk the semi-circles on the upper edges of the diamond. Voila, cardioid cake. Icing helps it look like one cake and not several discrete pieces, of course.
What I realized this time is that while I cut my square cakes into nine pieces, I tend to cut circular cakes into eight wedges. If I follow that with the heart-shaped cake (which I have so far - we're eating one piece each a day, this cake will last us a while), we will end up having 17 servings. Not equal servings, but are they ever? Not when I'm cutting.
I did the math and an eighth of the circle is less than a ninth of the square [pi/32 < 1/9]. However, I did not take into account what must be a difference in height because I used the same recipe for each "layer", implying that they should be of equal volumes, in which case 1/8 > 1/9. So, roughly equal is probably a pretty good approximation.
What I realized this time is that while I cut my square cakes into nine pieces, I tend to cut circular cakes into eight wedges. If I follow that with the heart-shaped cake (which I have so far - we're eating one piece each a day, this cake will last us a while), we will end up having 17 servings. Not equal servings, but are they ever? Not when I'm cutting.
I did the math and an eighth of the circle is less than a ninth of the square [pi/32 < 1/9]. However, I did not take into account what must be a difference in height because I used the same recipe for each "layer", implying that they should be of equal volumes, in which case 1/8 > 1/9. So, roughly equal is probably a pretty good approximation.
