The Other Side Of | Class 6 Mathematics Notes

A Pinch of History

This section provides a historical perspective on the development of integers, zero, and negative numbers.

It explains that negative numbers were first used in ancient Asia, particularly in China and India, mainly in accounting contexts. The Nine Chapters on Mathematical Art (Jiuzhang Suanshu) from China used red and black rods to represent positive and negative numbers.

In India, Kautilya's Arthaśhāstra (c. 300 BCE) discussed credit and debit, recognizing negative balances. The Bakśhālī manuscript (c. 300 CE) used a special symbol to denote negative numbers.

Brahmagupta (628 CE) gave the first general treatment of positive numbers, negative numbers, and zero as equally valid numbers with explicit rules for addition and subtraction. His rules include:

• Sum of two positives is positive.
• Sum of two negatives is negative.
• Sum of a positive and a negative is the difference with the sign of the larger.
• Sum of a number and its inverse is zero.
• Sum of any number and zero is the same number.

For subtraction, Brahmagupta stated:

• Subtracting a smaller positive from a larger positive is positive.
• Subtracting a larger positive from a smaller positive is negative.
• Subtracting a negative is the same as adding the corresponding positive.
• Subtracting a number from itself is zero.
• Subtracting zero leaves the number unchanged.

The section notes that negative numbers were slow to be accepted in Europe, with some mathematicians calling them 'absurd' even in the 18th century. However, today, zero and negative numbers are fundamental in mathematics and science, validating Brahmagupta's early insights.

📊 Diagram: Portrait of Brahmagupta and illustrations of positive and negative numbers using tokens and rods.

🧪 Activity: Explain Brahmagupta's rules using the Building of Fun or number line analogy and provide examples.

🔗 Connection: This historical understanding supports the formal rules and operations on integers studied in the chapter.