NCERT Book Class 9 Mathematics Chapter 1 Orienting Yourself: The Use of Coordinates

Orienting Yourself: The Use of
1 Coordinates

1.1 Introduction
A system of coordinates is a structured framework (like the grid lines on
a map or graph paper) that enables us to use numbers to describe the
exact physical locations of points or objects.
The idea of ‘grid-based thinking’ and the geometry required to
define the locations of points in space — indeed has deep roots in
Bhārat. The first systematic use of grids occurred thousands of years
ago — on a massive urban scale— in the Sindhu-Sarasvatī Civilisation,
where city streets were constructed with striking precision in
North–South and East–West directions at uniform distances of about
10 metres apart. This was a coordinate system in practice: a merchant
could find a shop or a warehouse by counting North–South and
East–West units of distance from the city centre. Baudhāyana (c. 800
C.E.), as we have seen, later used East–West and North–South lines for his
deep geometric constructions, developing the Baudhāyana–Pythagoras
Theorem and thus laying the foundation of coordinate geometry.
Putting coordinates on the Earth’s surface later became important
for navigation. Ujjayinī was described in the ancient world— at least
as early as the 4th century BCE in the early Siddhāntas— as the point
marking the central longitude meridian from which all other locations
were measured. The Greek mathematician Ptolemy (c. 150 BCE),
building on earlier works including that of Hipparchus, later described
the latitudes and longitudes of thousands of locations, including ‘Ozine’
(Ujjayinī). Āryabhaṭa (c. 499 CE) replaced the Greek ‘chords’ with ‘sines’,
making it much easier to calculate the coordinates of a star or a city.
He mapped the sky using Celestial Coordinates, measuring coordinate
distances from the ecliptic (the path of the sun).
Brahmagupta (c. 628 CE) formalised the notion and use of zero
and the negative numbers as algebraic entities; in modern coordinate
systems, the ‘origin’ is zero and the ‘negative axes’ represent values less
than zero. Without Brahmagupta’s work, the four-quadrant Cartesian
plane, as we will study in this chapter, would be impossible.