Frobenius's Theorem states that a real division algebra has a maximum of this many dimensions, and William Hamilton first described such a division algebra with this many total dimensions, which contains imaginary numbers represented as i, j, and k. The Heawood conjecture was proven for segmented planes to show that this many colors are sufficient to shade a map so that no same-colored regions bound each other.
Frobenius's Theorem states that a real division algebra has a maximum of this many dimensions, and William Hamilton first described such a division algebra with this many total dimensions, which contains imaginary numbers represented as i, j, and k. The Heawood conjecture was proven for segmented planes to show that this many colors are sufficient to shade a map so that no same-colored regions bound each other. For 10 points, name this smallest composite number, which is the square of the only even prime.
Frobenius's Theorem states that a real division algebra has a maximum of this many dimensions, and William Hamilton first described such a division algebra with this many total dimensions, which contains imaginary numbers represented as i, j, and k. The Heawood conjecture was proven for segmented planes to show that this many colors are sufficient to shade a map so that no same-colored regions bound each other.
{four}