Root system inner product is the Killing form. The cosine of the angle between two roots is constrained to be a half-integral multiple of a square root of an integer. This is because formula_32 and formula_33 are both integers, by assumption, and formula_34 Since formula_35, the only possible values for formula_36 are formula_37 and formula_38, corresponding to angles of 90°, 60° or 120°, 45° or 135°, 30° or 150°, and 0° or 180°. Condition 2 says that no scalar multiples of "α" other than 1 and -1 can be roots, so 0 or 180°, which would correspond to 2"α" or −2"α", are
How to Talk to a Liberal (If You Must) "never apologize to, compliment, or show graciousness to a Democrat". The book was on "The New York Times Best Seller list" for 17 weeks. How to Talk to a Liberal (If You Must) How to Talk to a Liberal (If You Must) is a 2004 book by Ann Coulter. The book is a collection of columns written by Coulter on liberalism, the war on terror, and the media. In it, Coulter offers advice gleaned from her experience as a political pundit. She attacks "The New York Times" and the Democratic Party, and sums up her opinion of liberals in two