Euclidean Geometry: A First Course by Mark Solomonovich

By Mark Solomonovich

This textbook is a self-contained presentation of Euclidean Geometry, an issue that has been a center a part of institution curriculum for hundreds of years. The dialogue is rigorous, axiom-based, written in a standard demeanour, real to the Euclidean spirit. alterations within the Euclidean airplane are incorporated as a part of the axiomatics and as a device for fixing building problems.

The textbook can be utilized for educating a highschool or an introductory point university path. it may be specially instructed for colleges with enriched mathematical courses and for homeschoolers trying to find a rigorous conventional dialogue of geometry.

The textual content is provided with over 1200 questions and difficulties, starting from basic to demanding. The options sections of the e-book comprise approximately two hundred solutions and tricks to options and over a hundred distinctive options concerning proofs and structures. extra options and a few vitamins for academics come in the Instructor’s handbook, that's issued as a separate book.

From the Reviews... ‘In phrases of presentation, this article is extra rigorous than any present highschool textbook that i do know of. it's in keeping with a method of axioms that describe occurrence, postulate a suggestion of congruence of line segments, and suppose the lifestyles of sufficient inflexible motions ("free mobility")…
My intestine response to the ebook is, would it be really good if American highschool scholars may be uncovered to this critical mathematical therapy of basic geometry, rather than the entire junk that's offered to them in latest textbooks.

This publication makes no concession to the TV-generation of scholars who wish (or is it the publishers who wish it for them?) beautiful images, aspect bars, puzzles, video games, historic references, cartoons, and all these coloured pictures that muddle the pages of a standard sleek textbook, whereas the mathematical content material is diluted an increasing number of with each one successive edition.’
Professor Robin Hartshorne, collage of California at Berkeley.

‘The textbook “Euclidean Geometry” by means of Mark Solomonovich fills an enormous hole within the plethora of mathematical textbooks – it presents an exposition of classical geometry with emphasis on common sense and rigorous proofs…
I will be overjoyed to work out this textbook utilized in Canadian faculties within the framework of a higher geometry curriculum. until eventually at the present time comes, I hugely suggest “Euclidean Geometry” by means of Mark Solomonovich for use in arithmetic Enrichment courses throughout Canada and the USA.’

Professor Yuly Billig, Carlton college

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Extra resources for Euclidean Geometry: A First Course

Sample text

For each of the following statements in the left column choose its negation from the statements in the right column. Substantiate your choice based on properties of complements. a) This animal is a dog. (i) This animal is a cat (ii) This is not an animal (iii) This animal is not a dog b) The expression in brackets is positive. (i) The expression in brackets is negative (ii) The expression in brackets is either negative or zero. (iii) The expression that stands outside the brackets is positive. c) This number is divisible by 5.

Also, −4 ≡ 1(mod 5) since −4 = 5 ⋅ (−1) + 1 (again, the remainder is 1), etc. a) Prove that the described relation is an equivalence relation. b) Consider the relation of congruence modulo 5 on the set of integers. In the above example we found that the numbers 6, 1, and – 4 are congruent to 1 modulo 5, that is they belong to [1] (of course, this class could be denoted [6] or [– 4] as well). } . Describe all the other equivalence classes of this relation. How many of them have you found? 55. Adduce examples of equivalence relations.

A person inside this rectangle illustrates the direct statement, the inhabitants of the Northern and Southern Alberta disprove, respectively, the converse and inverse, and a resident of the North West Territories supports the contrapositive statement. 1 We shall conclude this section with the summary of logical relations between a direct and the related conditional statements. 2-3 CŸH Inverse ⇔ H ŸC Questions and Problems. 1. In each of the following cases put a statement in the conditional form.

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