In 1856 Dirichlet made the following claim in a lecture:
Monthly Archives: April 2020
If Art+Math brings one person to mind, it’s Escher. His tessellations present the best-known instance, but he did a lot more than that.
We shall see that the lithograph can be viewed as drawn on a certain elliptic curve over the field of complex numbers…
I first learned as a kid that “there are only 17 basically different wallpapers” from W.W.Sawyer’s Prelude to Mathematics. (The quote appears on p.102. Aside: this remains an excellent gift for a youngster with a yen for math.) I remember my father pointing out the absurdity of this claim: are all mural wallpapers of van Gogh’s paintings basically the same?
The Resultant, Episode 3
Last time the linear operator
Φ: Kn[x]⊕Km[x] → Km+n[x]
made its grand entrance, clothed in the Sylvester matrix. (Recall that Kn[x] is the vector space of all polynomials of degree <n with coefficients in K, likewise for Km[x] and Km+n[x].)
The Resultant, Episode 1: Inside the Episode
In Episode 1 of our miniseries, “The Resultant”, the characters were introduced: integral domain R with fraction field K and extension field L, and polynomials E(x) and F(x) in R[x], factoring completely in L as a(x–u1)···(x–um) and b(x–v1)···(x–vn). (Repeated roots allowed.) We had our first formulas for the resultant: