Geometric Constructions in Number theory


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Paper must be written using LaTex. The most basic thing to remember is that this paper is about mathematics. It must have mathematical content at the college level. A paper with no serious mathematical content is not acceptable. *) A good paper will have the following features: 1) An introduction that gives good motivation to the topic. 2) Clearly written definitions of relevant terms (which may also be described in less formal language). 3) Careful mathematical reasoning that takes the reader from the definitions to some nontrivial mathematical results. This usually is placed in the format of theorems and proofs. 4) Examples that illustrate the basic mathematical ideas, including counterexamples that show how things break down if some hypotheses are not satisfied. Show a clear mastery of the material. **) In short:introduce ideas with motivation, state results, prove them, and illustrate what they mean by well-chosen examples. *)Paper should not contain the following: 1) A laundry list of examples, definitions, and theorems with no clear train of thought connecting them or moving in the direction of some goal. 2) Two or three equations and otherwise no actual mathematical content. (For instance, a paper on baseball statistics that has only a formula for the standard deviation or paper on shooting pool that only mentions the angle of incidence equals the angle of reflection, with no deeper mathematical development, is not acceptable.) 3) A persistent vagueness about the concepts being discussed or incomplete mathematical arguments. 4) A nonstandard tone (autobiographical, poetic, whimsical) 5) Errors in mathematics, history, or grammar. Proofread, and do not count on a spellchecker finding all the mistakes on its own.



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