# Some basic mathematics

Foundations of Mathematics: Some basic mathematics

Zero:
Zero is neither positive nor negative and is considered an even number.

Numbers:

• Whole numbers initiate from zero.
• Positive numbers are greater than zero, while negative numbers are less than zero.

Natural Numbers:

• Natural numbers, also known as counting or cardinal numbers, commence from 1.

Number 1:

• 1 is a natural and whole number.
• Not prime, not composite; the only positive integer neither prime nor composite.

Numbers:

• The smallest prime number is 2.
• The smallest composite number is 4.
• Integers encompass positives, negatives, and zero but exclude decimals and fractions.

Numeral and Place Value:

• A numeral is a group of digits.
• Place value indicates the local value of a digit based on its place.
• Face value denotes the actual value of a digit.

Types of Numbers:

• Natural numbers start from 1.
• Ordinal numbers signify order (first, second, third, etc.).
• Whole numbers include zero and all natural numbers.
• Integers encompass natural, positive, negative numbers but exclude decimals and fractions.
• Non-negative integers: 0, 1, 2, 3…
• Non-positive integers: 0, -1, -2, -3…
• Prime numbers have only two factors (1 and itself).
• Composite numbers have more than two factors and are not prime.
• Even numbers are divisible by 2.
• Odd numbers are not divisible by 2.
• Co-prime numbers share a highest common factor of 1.
##### Rational Numbers:
• Expressible as P/Q, where P and Q (Q≠0) are integers.
• Include perfect squares, terminating decimals, and repeating decimals.
##### Irrational Numbers:
• Real numbers that cannot be expressed as a fraction of two integers.
• Examples: √2 and π.

Real Numbers:

• A combination of rational and irrational numbers.
• A complete representation of the number system.

Angle Concepts:

• A straight line angle measures 180 degrees.
• The sum of all angles in a triangle is 180 degrees.
• A circle has 360 degrees.
• A rectangle also has 360 degrees.
• A complete angle measures 360 degrees.

Types of Angles:

• Acute: measures less than 90 degrees.
• Right: measures exactly 90 degrees.
• Obtuse: measures between 90 and 180 degrees.
• Reflex: measures between 180 and 360 degrees.

Triangles:

• The sum of all angles in a triangle is 180 degrees.

Types of Triangles (based on Side Length):

• Equilateral: all sides are equal.
• Isosceles: two sides are equal.
• Scalene: all sides and angles are unequal.

Types of Triangles (based on Angle Measurement):

• Acute: all angles measure less than 90 degrees.
• Right: one angle measures exactly 90 degrees.
• Obtuse: one angle measures greater than 90 degrees.
##### Angle Relationships:
• Complementary angles sum up to 90 degrees.
• Supplementary angles sum up to 180 degrees.
• Adjacent angles share a vertex and a common arm.

Right Angles and Triangles:

• A right angle measures 90 degrees.
• A right triangle contains one right angle.

Lines and Line Segments:

• A line consists of infinite points.
• A line segment is part of a line with two endpoints.

Angle Vertex:

• The vertex of an angle is the common endpoint of two rays forming the angle.

Circle Properties:

• Circumference: distance around a circle.
• Diameter: distance from one side to the other, passing through the center.
• π (pi): ratio of the circumference to diameter, approximately 3.14.
• A polygon with four sides and four vertices.
• Can be regular or irregular.
• Sum of interior angles is 360°.

Square:

• A quadrilateral with all four sides equal, opposite sides parallel, and all angles equal to 90°.

Rectangle:

• A quadrilateral with all four sides equal, opposite sides parallel, and all angles equal to 90°.

Parallelogram:

• Opposite sides equal and parallel.
• Opposite angles equal.
• No angle measures 90 degrees.

Rhombus:

• Four equal sides.
• Opposite sides parallel.
• Opposite angles equal.
• No angle measures 90 degrees.

Trapezium:

• Only one pair of opposite sides parallel.

Kite:

• Two pairs of adjacent equal sides.
• One pair of equal angles.

Perimeter and Area:

• Perimeter is the boundary distance.
• Area is measured in square units.

Rectangle:

• Perimeter: 2(length + width).
• Area: length × width.

Square:

• Perimeter: 4 × side or sum of all sides (a + a + a + a).
• Area: side × side.

Circle:

• Circumference (Perimeter): π × diameter.

Calculation Example:
Given length (L) and width (W) of a rectangle are 5.3 cm each:

• Perimeter: 2(L + W) = 2(5.3 + 5.3) = 21.2 cm.
• Area: L × W = 5.3 × 5.3 = 28.09 cm².

Conversion: Fahrenheit to Celsius:

• C = (F – 32) × (5/9).

Conversion: Celsius to Fahrenheit:

• F = (C × 9/5) + 32.

Part/Whole Percentage:

• Percentage = (part/whole) × 100.

Cross Multiplying:

• A method to find missing values in proportions.

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Some basic mathematics