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Prove, by induction, that the sum of the angles of a convex n-gon (with n 3) is 180.n 2/

Mathematics: A Discrete Introduction | 3rd Edition | ISBN: 9780840049421 | Authors: Edward A. Scheinerman ISBN: 9780840049421 447

Solution for problem 22.10 Chapter 22

Mathematics: A Discrete Introduction | 3rd Edition

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Mathematics: A Discrete Introduction | 3rd Edition | ISBN: 9780840049421 | Authors: Edward A. Scheinerman

Mathematics: A Discrete Introduction | 3rd Edition

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Problem 22.10

Prove, by induction, that the sum of the angles of a convex n-gon (with n 3) is 180.n 2/ degrees, i.e., .n 2/ radians.

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Adequately Defined Variables Variable: A symbol used to represent a particular mathematical or logical entity with a particular value Variable Declaration: A statement stating that a certain symbol will be used to represent a particular mathematical or logical entity Adequately Defined Variables: Variables with unambiguously specified entities and values ◦ Entity Examples: Integer, Real Number, etc. Global vs Local Variables Global Definition: If the declaration of a variable’s entity and the setting of its value is preserved throughout an argument, unless its value is reset by a global redefinition Local Definition: If the declaration of a variable’s entity and the setting of its value is meaningful for only a limited section of an argument, after which the symbol loses the previous definition and must be redefined before it can meaningfully be used again ◦ Example: If­then statements ◦ Note: A variable is not adequately defined if it is only declared in an if­ then statement Congruence (mod n) – congruence: Let n be a positive integer, and suppose that a and b are any integers… ◦ “a is congruent to b modulo n (“a = b (mod n)”) if and only if a – b is an integer multiple of n” ◦ Theorem: “a = (a + n)(mod n) and a = (a – n)(mod n)” ◦ Corollary: “a = (a + bn)(mod n) Statements in Logic  Statement: A sentence that is true or false, but not both

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Chapter 22, Problem 22.10 is Solved
Step 3 of 3

Textbook: Mathematics: A Discrete Introduction
Edition: 3
Author: Edward A. Scheinerman
ISBN: 9780840049421

Since the solution to 22.10 from 22 chapter was answered, more than 237 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Mathematics: A Discrete Introduction, edition: 3. This full solution covers the following key subjects: . This expansive textbook survival guide covers 69 chapters, and 1110 solutions. Mathematics: A Discrete Introduction was written by and is associated to the ISBN: 9780840049421. The full step-by-step solution to problem: 22.10 from chapter: 22 was answered by , our top Math solution expert on 03/15/18, 06:06PM. The answer to “Prove, by induction, that the sum of the angles of a convex n-gon (with n 3) is 180.n 2/ degrees, i.e., .n 2/ radians.” is broken down into a number of easy to follow steps, and 24 words.

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Prove, by induction, that the sum of the angles of a convex n-gon (with n 3) is 180.n 2/