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Zero is the most prominent invention of humankind- it is the basis of everything from modern electronics, computers, and calculus to automation and everything in between that you can think of. But you might not know about the incredible evolution of zero. In this blog, we will help you understand the fascinating impact of zero on mathematics, but before that, let us first reveal the history of zero.

The story of zero

You will feel proud to know that Indian mathematicians introduced zero to the numerical system in the 5th century BC. Aryabhata, a renowned Indian astronomer and mathematician, used a distinct symbol to denote emptiness, void, or shunya.

However, it is not the zero that we are using today in mathematics. After him, Brahmagupta, another leading light in the field of mathematics and astronomy, expanded the concept of zero and established rules for its operations in mathematics in the 7th century BC.

Brahmagupta, in his work, “Brahmasputasiddhanta”, proposed rules for arithmetic, which involve zero and negative numbers. His rules made the foundation of elementary arithmetic that we study. For example, he was the one who stated that the addition of two negative numbers results in a negative number, and the addition of two positive numbers results in a positive number.

Below is a summary of some of his rules

1. The addition of a negative number with zero results in the negative number itself. Similarly, the addition of a positive number with zero results in the same positive number.

2. The addition of a positive number and a negative number is actually their difference. And if the positive and negative numbers are equal, the sum is zero.

3. The multiplication of a positive and a negative number is negative, while the product of a negative and negative and positive and positive number is positive.

4. Multiplication of zero with either a positive or negative number results in zero.

5. A positive number, when divided by a negative number, results in a negative number. Similarly, a negative number divided by a positive number results in a negative number.

6. The square root of a positive as well as a negative number is positive, and the square root of zero is zero.

Brahmagupta also used mathematical findings for astronomical computations, such as calculating the position of heavenly bodies and more. Along with this, he also introduced quadratic equations and laid the foundation of Algebra.

How does Zero reach Arabia and Europe?

Arabian voyagers took the concept of zero with themselves to their cities and towns. In the 9th century, a Persian scholar and mathematician, Mohammed ibn-Musa al-Khowarizmi, worked on the concept of zero and Indian numerals and made significant contributions to several mathematical concepts, including algebra. However, in Europe, the acceptance and understanding of the zero faced some resistance. This was because the Roman numeral system did not represent zero in their calculations. But in the 12th century, Italian mathematician Fibonacci introduced the Hindu-Arabic numeral system to Europe with a book called Liber Abaci.

The significance and the impact of zero in mathematics

Zero helped revolutionize mathematical concepts such as algebra, arithmetic, and calculus. It enabled precise calculations and helped us understand complex mathematical concepts. Zero assisted us in understanding nothingness and infinity and encouraged us to ask ourselves the fundamental question of reality and existence.

Zero impacted mathematics as well as several other fields, such as philosophy, science, and technology. However, its impact on mathematics was the most profound. Let us explore some key impacts and applications of zero in mathematics.

1. Arithmetic

Calculations such as addition and subtraction require borrows and carry, which is not possible without a zero. When it comes to multiplication, a product of zero with any number leads to zero. But division with zero results in undefined results or infinity, which leads to many complexities and contradictions and plays an essential role in higher mathematics.

2. Algebra and calculus

Algebraic equations can not be expressed without a zero. This is because, in algebra, unknown values are found by setting equations to zero. Similarly, in calculus, zero helps determine the behaviors of functions by determining the limit of a function f(x) as x approaches zero. Algebra and calculus are an essential part of the curriculum of the best CBSE schools in Baddi, which means you will get a complete grasp of the concepts of functions and limits discussed here in this article at your school.

3. Geometry

Cartesian geometry, a fundamental concept in geometry, uses zero as a reference point. The origin (0,0) is the point where the X-axis and Y-axis intersect. In two dimensions, it is represented as the (0,0), and in three dimensions, it is represented as (0,0,0). X is the horizontal coordinate, while Y is the vertical coordinate in Cartesian geometry.

4. Place value notation

Zero plays a crucial role as a placeholder that helps represent the value of each digit by its position. For example, if we consider the number 89, the digit 9 is in the one's place, so its place value is 9*1=9, and digit 8 is in ten places, so its place value is 8*10=80. So, the overall value is 80+9=89. Also, we can not express numbers like 10, 100, 1000 without zero.

5. Computer science and engineering

Zero is the foundation of the digital system- As they run on the 0’s and 1’s, which represent on and off. Moreover, zero and one are the building blocks of digital circuits where 0 represents low voltage or off state and 1 represents on state or high voltage. Zero is also used as a fundamental concept in thermodynamics, signal processing, and electrical engineering.

The extent to which zero is used extends to the field of mathematics and several other prominent fields. Without zero, it is impossible to understand the universe, technological advancements, and philosophy.

Conclusion

The invention of zero significantly impacted humankind by opening the doors to several mathematical concepts. It paved the way for developments in diverse fields, such as physics, computer science, engineering, and technology. And it is still helping us by unfolding more layers of scientific understanding.