|© | Dror Bar-Natan: Classes: 2014-15: Math 475 - Problem Solving Seminar:||(27)||
Next: Blackboards for Thursday February 12
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Reading. Sections 1.6 and 1.7 of Larson's textbook.
Next Quiz. Tuesday February 24, on these two sections.
Problem 1. Prove: You cannot colour the points of the plane with just three colours, so that no two points of distance 1 will be coloured with the same colour. What if you had four colours available?
Problem 2 (Larson's 1.6.2).
Problem 3 (Larson's 1.7.1). Prove that an angle inscribed in a circle is equal to one half the central angle which subtends the same arc, as in the picture on the right.
Problem 4 (Larson's 1.7.8). Determine $F(x)$, if for all real $x$ and $y$, $F(x)F(y)-F(xy)=x+y$.