A Square and A Cube - Vocabulary Flashcards

Vocabulary flashcards defining key mathematical terms and historical concepts from Grade 8 Mathematics Chapter 1: A Square and A Cube.

Square Number

A number that can be expressed as the product of a number with itself, denoted as $n \times n = n^2$.

Perfect Squares

Numbers that are the squares of natural numbers, such as $1$, $4$, $9$, $16$, and $25$.

Partner Factor

A factor of a given number that pairs with another factor such that the product of the pair equals the given number.

Square Root

For a number $y$, if $y = x^2$, then $x$ is the square root of $y$, denoted as $\sqrt{y}$.

Triangular Numbers

Numbers represented by triangular dot patterns (such as $1$, $3$, $6$, $10$, and $15$), where the sum of any two consecutive triangular numbers forms a square number.

Cube Number

A number obtained by multiplying a number by itself three times, written as $n \times n \times n = n^3$.

Perfect Cubes

Numbers that are obtained by multiplying a natural number by itself three times, such as $1$, $8$, $27$, and $64$.

Taxicab Numbers

Numbers that can be expressed as the sum of two positive cubes in two different ways.

Hardy–Ramanujan Number

The number $1729$, which is the smallest taxicab number, expressible as $1^3 + 12^3$ and $9^3 + 10^3$.

Cube Root

For a number $y$, if $y = x^3$, then $x$ is the cube root of $y$, denoted by $\sqrt[3]{y}$.

Varga

An ancient Sanskrit term used for a square figure, its area, or the square power ($n^2$).

Ghana

An ancient Sanskrit term used for a solid cube as well as the product of a number with itself three times ($n^3$).

Varga-varga

An ancient Sanskrit term used to denote the fourth power of a number ($n^4$).

Mula

A Sanskrit word meaning root of a plant, basis, cause, or origin, used in ancient India for the mathematical operation of taking roots.

Varga-mula

The ancient Sanskrit term for square root, meaning the basis, cause, or origin of the square.

Ghana-mula

The ancient Sanskrit term for cube root, meaning the basis, cause, or origin of the cube.

Pada

An ancient Sanskrit term meaning foot, basis, cause, or origin, used by mathematicians like Brahmagupta to denote the root of a square ($krti$).