Orienting Yourself: The Use of Coordinates

Flashcards covering the history, major historical figures, and fundamental terminology of coordinate geometry as presented in the lecture notes.

System of coordinates

A structured framework (like grid lines on a map) that enables the use of numbers to describe the exact physical locations of points or objects.

Sindhu-Sarasvatī Civilisation

Ancient civilisation where the first systematic use of grids occurred on a massive urban scale, with streets constructed in North-South and East-West directions about $10\,m$ apart.

Baudhāyana

An ancient scholar (c. $800\,CE$) who used East-West and North-South lines for geometric constructions and developed the Baudhāyana–Pythagoras Theorem.

Ujjayinī

The point described as early as the $4\text{th century BCE}$ in the early Siddhāntas as the central longitude meridian from which all other locations were measured.

Ozine

The name used by the Greek mathematician Ptolemy (c. $150\,BCE$) to refer to Ujjayinī.

Āryabhaṭa

A mathematician (c. $499\,CE$) who replaced Greek 'chords' with 'sines' and mapped the sky using Celestial Coordinates measured from the ecliptic.

Brahmagupta

The scholar (c. $628\,CE$) who formalised the notion of zero and negative numbers as algebraic entities, making the four-quadrant Cartesian plane possible.

Arin

The name given to the Ujjayinī meridian in Arabic geography, which served as the zero-longitude reference for early Arabic maps.

Al-Bīrūnī

An influential Arab scholar (c. $1000\,CE$) who used Indian trigonometric methods to calculate city coordinates and perfected the 'astrolabe' for navigation.

Ömar Khayyām

A mathematician (c. $1100\,CE$) who was the first to solve algebraic problems using geometry by interpreting them as coordinates in a plane.

René Descartes

The scholar (c. $1637\,CE$) who formalised that any point in a two-dimensional plane could be defined by two numbers representing distances from two perpendicular axes.

x-axis

The horizontal line used in a two-dimensional coordinate system.

y-axis

The vertical line used in a two-dimensional coordinate system.

Origin

The point of intersection of the x-axis and y-axis, denoted by $O(0, 0)$.

Cartesian plane

The plane in which the coordinate axes are situated, also called the coordinate plane or the xy-plane.

Quadrants

The four parts into which the coordinate axes divide the Cartesian plane.

x-coordinate

The perpendicular distance of a point $P$ from the y-axis, measured along the x-axis.

y-coordinate

The perpendicular distance of a point $P$ from the x-axis, measured along the y-axis.

Quadrant I

The quadrant where both the x-coordinate and y-coordinate are positive ($+, +$).

Quadrant II

The quadrant where the x-coordinate is negative and the y-coordinate is positive ($-, +$).

Quadrant III

The quadrant where both the x-coordinate and y-coordinate are negative ($-, -$).

Quadrant IV

The quadrant where the x-coordinate is positive and the y-coordinate is negative ($+, -$).

Distance Formula

Based on the Baudhāyana–Pythagoras Theorem, the distance between points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.