Patterns in Mathematics and Geometry

This set of flashcards covers vocabulary and fundamental concepts from the lecture notes on mathematical patterns, geometry (lines and angles), arithmetic operations, data handling, and factors and multiples.

Patterns in Numbers

A sequence where the numbers follow a specific rule identified by observing the change from one number to the next.

Natural Numbers

Also known as counting numbers, following the rule of starting with $1$ and adding $1$ to get the next term ($1, 2, 3, 4, 5, \text{...}$).

Even Numbers

Numbers that are divisible by $2$. The sequence starts at $2$ and adds $2$ to get each subsequent term.

Odd Numbers

Numbers that are not divisible by $2$. The sequence starts at $1$ and adds $2$ to get each subsequent term.

Triangular Numbers

Numbers that can be represented as a triangle using dots, where the $n^{th}$ term is obtained by adding the first $n$ natural numbers ($1, 3, 6, 10, 15, \text{...}$).

Virahanka Numbers

A sequence starting with $1$ and $2$ where each subsequent number is the sum of the previous two numbers ($1, 2, 3, 5, 8, \text{...}$).

Square Numbers

Numbers produced by multiplying a number by itself, which can be represented as a square using dots ($1, 4, 9, 16, 25, \text{...}$).

Cube Numbers

Numbers obtained by multiplying a number by itself twice, which can be arranged in the form of a perfect cube using blocks ($1, 8, 27, 64, 125, \text{...}$).

Power of 2 Numbers

A sequence starting with $1$ where each term is multiplied by $2$ to get the next term ($1, 2, 4, 8, 16, \text{...}$).

Number Theory

The branch of mathematics that studies patterns in whole numbers.

Hexagonal Numbers

A sequence of numbers that can be represented as a hexagon with dots ($1, 7, 19, 37, \text{...}$).

Collatz Sequence

A sequence starting with any whole number: if even, divide by $2$; if odd, multiply by $3$ and add $1$. All such sequences eventually end with the number $1$ according to the Collatz Conjecture.

Regular Polygon

A geometric shape with all sides of equal length and all interior angles of equal measure.

Complete Graph

A graph where every point (vertex) is connected to every other point by a line (edge).

Koch Snowflake

A geometric fractal shape made by starting with a triangle and repeatedly adding smaller triangles to each side so that any zoomed-in part resembles the whole shape.

Palindromic Numbers

Numbers that read the same from left to right as they do from right to left (e.g., $121$, $2332$).

Line

A geometric figure that does not have a fixed length and extends endlessly in both directions.

Line Segment

A portion of a line that has a fixed length and two end points.

Ray

A figure that has a starting point and extends endlessly in one other direction.

Parallel Lines

Lines that have the same distance between them at all times and never meet. Denoted by the sign $\parallel$.

Intersecting Lines

Two lines that meet or cross each other at a specific point called the point of intersection.

Perpendicular Lines

Two lines that meet each other at an angle of $90^\text{o}$. Denoted by the sign $\perp$.

Angle

A figure formed by the rotation of a ray about a point, with the extent of rotation measured in degrees ($^\text{o}$).

Initial Ray

The ray in its position before rotation begins for an angle.

Terminal Ray

The ray in its position after rotation has occurred for an angle.

Vertex

The point about which a ray rotates to form an angle.

Interior of an Angle

The region consisting of all points that lie between the arms of the angle.

Acute Angle

An angle measuring between $0^\text{o}$ and $90^\text{o}$.

Right Angle

An angle measuring exactly $90^\text{o}$.

Obtuse Angle

An angle measuring between $90^\text{o}$ and $180^\text{o}$.

Straight Angle

An angle measuring exactly $180^\text{o}$.

Reflex Angle

An angle measuring between $180^\text{o}$ and $360^\text{o}$.

Complete Angle

An angle measuring exactly $360^\text{o}$.

Protractor

A semicircular tool used to draw and measure angles from $0^\text{o}$ to $180^\text{o}$.

Angle Bisector

A ray that passes through the vertex of an angle and divides it into two equal parts.

Kaprekar Constant

The special number $6174$ reached by repeatedly subtracting the smallest number from the greatest number formed by a set of four digits.

BDMAS Rule

A rule defining the order of arithmetic operations: Brackets, Division, Multiplication, Addition, and Subtraction.

Raw Data

Data that exists as a random list of items or values exactly as it was collected.

Frequency

The count of each category within a specific data set.

Infographics

Visual representations of information that make data simple and easy to understand.

Factor

A number that divides another number completely, leaving a remainder of $0$. Every factor is less than or equal to the number.

Multiple

A number built by adding a number repeatedly. Every multiple is greater than or equal to the number.

Prime Number

A number that has exactly two factors: $1$ and itself.

Composite Number

A number that has more than two factors.

Prime Factorisation

The process of expressing a composite number as a product of its prime factors.

HCF (Highest Common Factor)

The greatest factor common to two or more given numbers.

LCM (Least Common Multiple)

The smallest (least) of the common multiples of two or more given numbers.

Perimeter

The length of the boundary of a closed $2\text{D}$ shape.

Area

The amount of space enclosed by a $2\text{D}$ shape (surface).