**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.

**Quadrilateral:**

- 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.
- Area: π × radius².

**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.

For more comprehensive mathematics resources, visit RanaMaths.com

Some basic mathematics