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Handbook of mathematics for engineers and scienteists part 6

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A plane triangle, or simply a triangle, is a plane figure bounded by three straight line segments (sides) connecting three noncollinear points (vertices) (Fig. 3Aa). The smaller angle between the two rays issuing from a vertex and passing through the other two vertices is called an (interior) angle of the triangle. | Chapter 1 Arithmetic and Elementary Algebra 1.1. Real Numbers 1.1.1. Integer Numbers 1.1.1-1. Natural integer even and odd numbers. Natural numbers 1 2 3 . all positive whole numbers . Integer numbers or simply integers 0 1 2 3 . Even numbers 0 2 4 . all nonnegative integers that can be divided evenly by 2 . An even number can generally be represented as n 2k where k 0 1 2 . Remark 1. Sometimes all integers that are multiples of 2 such as 0 2 4.are considered to be even numbers. Odd numbers 1 3 5 . all natural numbers that cannot be divided evenly by 2 . An odd number can generally be represented as n 2k 1 where k 0 1 2 . Remark 2. Sometimes all integers that are not multiples of 2 such as 1 3 5.are considered to be odd numbers. All integers as well as even numbers and odd numbers form infinite countable sets which means that the elements of these sets can be enumerated using the natural numbers 1 2 3 . 1.1.1-2. Prime and composite numbers. A prime number is a positive integer that is greater than 1 and has no positive integer divisors other than 1 and itself. The prime numbers form an infinite countable set. The first ten prime numbers are 2 3 5 7 11 13 17 19 23 29 . A composite number is a positive integer that is greater than 1 and is not prime i.e. has factors other than 1 and itself. Any composite number can be uniquely factored into a product of prime numbers. The following numbers are composite 4 2x2 6 2x3 8 23 9 32 10 2 x 5 12 22 x 3 . The number 1 is a special case that is considered to be neither composite nor prime. 1.1.1-3. Divisibility tests. Below are some simple rules helping to determine if an integer is divisible by another integer. All integers are divisible by 1. Divisibility by 2 last digit is divisible by 2. Divisibility by 3 sum of digits is divisible by 3. Divisibility by 4 two last digits form a number divisible by 4. Divisibility by 5 last digit is either 0 or 5. 3 4 Arithmetic and Elementary Algebra Divisibility by 6 divisible by both 2 .