Hello Students, This is the chapter of 9th class The world of number , where now you connect with me. I will discuss about introduction of this chapter because this is one of the most important chapter of your 9th class new ncert book and syllabus.
In this chapter , there are many important topic . That you will read later in this chapter .
3.1. The Dawn of Mathematics: The Human Need to
Count
Long before humanity built cities, formulated laws, or studied the stars,
there existed a fundamental, practical necessity: the need to keep count.
Mathematics did not begin in a classroom with equations on a board; it
began in the dirt, on the bark of trees, and on bones.
Imagine you are living thousands of years ago in a small agricultural
settlement along the banks of the Saraswati river. You have a herd
of cattle. Every morning, they go out into the dense forests to graze,
and every evening, they return. How do you ensure that a calf has
not wandered off? Without words for numbers, and without written
symbols, early humans solved this through a concept called one-to-one
correspondence.
For every cow that left the settlement, the herder might place one
pebble in a clay pot. In the evening, for every cow that returned, one
pebble was removed. If the pot was empty at the end of the day, the herd
was safe. If pebbles remained, cows were missing. This simple act of
matching one object to another was the birth of the Natural Numbers
( = {1, 2, 3, 4, … }).
3.1.1 A History Written in Bone
While the decimal place-value system we use today was perfected in
the Indian subcontinent, the earliest physical evidence of humanity
recording natural numbers takes us deep into the heart of Africa. The
first mathematicians did not use paper; they used tally marks carved
into bone.
The Lebombo Bone, discovered in the Lebombo Mountains
between South Africa and Swaziland, dates back approximately
35,000 years. It is a bone featuring 29 distinct, deliberately-carved
uniformly-sized notches. Anthropologists and mathematicians believe
this was not just random scratching, but a tool used as a lunar phase
counter or a menstrual calendar, indicating that early humans were
tracking time through natural numbers.
Even more fascinating is the Ishango bone, found near the
headwaters of the Nile River in the Democratic Republic of Congo,
dating to around 20,000 BCE. This bone contains three columns of
asymmetrical notches. What makes the Ishango bone a mathematical
marvel is the specific grouping of the tallies. One of the columns groups
notches into 11, 13, 17, and 19 — the prime numbers between 10 and
20. Another column seems to demonstrate the concept of multiplication
by 2 (doubling). These artefacts indicate that the abstract concept of a
‘number’ is indeed tens of thousands of years old.
3.1.2 The Indian Context: Trade and Astronomy
As civilisations advanced, so did the need for larger numbers. In the
ancient urban centers of the Indus Valley Civilisation, such as Lothal
and Harappa, standardised weights and measures were crucial for
trade. A merchant trading terracotta pottery, lapis lazuli, or cotton
with Mesopotamia needed a robust system of accounting.
During Vedic times, Indian philosophers were fascinated by and
deeply pondered large numbers. In the Vedas, which go back thousands
of years, names were given to all powers of 10 up to 1012 (which was
called parārdha). In the Lalitavistara in the 4th century BCE, Buddha
describes names up to 1053, which is called tallakṣhaṇa.
Expressing quantities in terms of powers of 10 was explicitly used in
the Ṛigveda, thus setting the stage for the number system based on
powers of 10 to be developed in India in the ensuing years, and which
we now use around the world today. The development of the Indian
numeral system in terms of place values and powers of 10 also helped
pave the way for what is perhaps the most important mathematical
invention in human history: the concept of zero.