for a party tonight, i'd promised to bring lemon-meringue tartlets (don't go acting all impressed - they're surprisingly easy to make). i already had about two cups of lemon curd leftover from making spiced shortbread cookies earlier this week (don't you wish you were my roommate?), so i spun by the grocery store to pick up some ingredients for the crusts. at the grocery store, smiling from the produce section, were the most beautiful lovely grapefruits ever.
grapefruit-meringue tartlets! sang the lightbulb that flashed on over my head. so i bought four grapefruits and another pound of butter and carried on my merry way.
i make lemon curd kind of a lot, considering it's, you know, lemon curd. but as someone who doesn't love chocolate, i make lemon bars and lemony sandwich cookies and lemon pies with moderate frequency. so the recipe exists in my head, rather than on a piece of paper, and i do most of it by sight and feel. for example, i have no idea how much lemon zest and lemon juice i use, i just know that it's about the quantity you get from three large lemons.
so, fuck. how do i convert lemons
answer: math! for zest equivalents, i simply need to figure out how to convert the surface area of an ellipsoid (the lemon) to that of a sphere (the grapefruit), and for juice equivalent i need to convert the volume of an ellipsoid (minus the pith) to the volume of a sphere (minus the pith).
this should be a walk in the park, right?
there was a leftover lemon on my counter. i wrapped it with a piece of string going around the round part (5.7 inches)and going around the long part (7.3 inches) and figured i would just plug it into some sort of simple equation to figure out the surface area.
the surface area of an ellipsoid is derived via this formula:
where a is width/2, b is length/2, and c is depth/2. or whatever. anyway, this is totally doable. knowing that the circumference of a lemon is 5.7 inches, we simply divide by pi (oh my god the puns are making themselves), getting both a width and depth of 1.814 inches.
it would be easy to measure the length of the lemon using my piece of string, but i stupidly cut the lemon up to make preserved lemons after i measured the two big circumferences. so time to convert the circumference of what i will assert is a perfect ellipse into the length of its major axis!
7.3 inches in circumference and a 1.814-inch transverse axis... and now we just plug it into this formula:
...and then we kill ourselves.
at this point i realized that it's been about 8 years since i've taken a math class that actually involved numbers, and i can't go on. so i did something shameful: i took my piece of string and i laid it out on the table in an ellipse that vaguely resembled what i thought the lemon looked like, and i measured its length, arriving at the oh-so-precise conclusion of "eh, 3 inches."
okay. now let's party. The volume of an ellipse that's 3" x 1.814" x 1.814" equals? 4/3 x 3.1415 x 1.5 x 0.907 x 0.907 = 5.168.
WE HAVE MEASUREMENT! except i forgot to include the depth of the pith, except fuck it i no longer care.
now it's time to measure the volume of the grapefruit. this is easy, because i am asserting that a grapefruit is a sphere, with a diameter of 13.2 inches. if the diameter is 13.2 then the radius is 2.05, so the volume is (dundundunnnn) 36.08.
this sounds obscenely large but i decided to just go with it. except that - while lemons have teeny pith (only about an eigth of an inch), grapefruits have giant massive pith. so i have to reduce my diameter by an inch, which means my radius by half an inch, which means my new equation becomes:
4/3 x 3.1415 x 1.55 x 1.55 x 1.55
which gives us a grapefruit volume of 15.6!
so a grapefruit (15.6) divided by a lemon (5.168) equals 3.01, which is close enough to 3 for me to say that the answer is:
THREE. THREE LEMONS = ONE GRAPEFRUIT.
easy as (oh my god, can i really say it?) easy as (wait for it!) easy as (here it comes... are you ready? come on... come on...)
easy as pi.