In measure theory, a branch of mathematics, the ham sandwich theorem, also called the Stone–Tukey theorem after Arthur H. Stone and John Tukey, states that given n measurable "objects" in n-dimensional space, it is possible to divide all of them in half (with respect to their measure, i.e. volume) with a single (n − 1)-dimensional hyperplane. Here the "objects" should be sets of finite measure (or, in fact, just of finite outer measure) for the notion of "dividing the volume in half" to make sense.
Read more about Ham Sandwich Theorem: Naming, History, Reduction To The Borsuk–Ulam Theorem, Measure Theoretic Versions, Discrete and Computational Geometry Versions
Famous quotes containing the words ham, sandwich and/or theorem:
“We had some ham and eggs and took our time saying goodbye to the bright lights.”
—Stanley Kubrick (b. 1928)
“I tell people all the time, you have to be in love with that pot. You have to put all your love in that pot. If you’re in a hurry, just eat your sandwich and go. Don’t even start cooking, because you can’t do anything well in a hurry. I love food. I love serving people. I love satisfying people.”
—Leah Chase (b. 1923)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)