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All About The Number Zero In Maths!

By Ava, published on 26/02/2019 Blog > Academia > Maths > The History Of Zero And Its Use In Maths!

Every student in every classroom across the world knows that if they get a zero on their maths homework or on a maths exam that they are in big trouble. The Zero, in this case, is synonymous with failure as they were unable to solve problems correctly out of all of the questions that were asked.

But the zero is used in many more places than just the classroom grading system, it is part of our whole society. Prices of things in shops, license plates, numbers to call, numbers in your bank account when you are broke. But all fun aside zero is a significant number that has the meaning of nothing but to us really means everything since it is perhaps the most used number in the math curriculum.

But when reading the number zero not many people think about its history or about the mathematician who introduced the number to modern mathematics. To become fluent in the language of mathematics you have to delve deeper than the surface. Math concepts like algebra, geometry, complex numbers, Pythagorean theorem, Linear equations, probability, Pi, special number Euler’s e, trigonometry (trig.), Equivalent fractions, the special number i, the golden ratio, and must be part of your math learning in your grade level math education. Let’s start by taking a closer look at the number 0.

zero is also a numerical digit As we understand it today, the number zero is neither a positive or negative number. Photo Source: Unsplash

The Perception Of Zero In History

Today the number zero in the numeral system is used to represent the absence of object or quantity. Each student learns the number 0 from primary school, learning it with the number system for counting, mathematically, with negative numbers and whole numbers.

As we understand it today, the number zero is neither a positive or negative number and as well as being a number it is also a numerical digit. But it was not always like this, zero has developed throughout history and changed with the changing ideas of the culture.

  1. The ancient Greeks believed that existence began with 1, and anything less than one to be impossible to write due to the fact that it didn’t exist. So the Ancient Greeks had no writing system including zero in their numeral system.
  2. The Babylonians began using zero to distinguish the void between numbers. So instead of writing 3 5, they added the zero in the middle making 305.
  3. The Mayans used zero between numbers, to express durations and to mark the dates of the calendar.
  4. The Indians used zero as if it were any other number and it is from India that the concept of zero was introduced although it took time to be accepted.
  5. The Arabians adopted the number calling it Sifr and take it to mean emptiness and also infinity.
  6. The Italians introduced it in Europe by translating it into Latin as Zephirum.

Zero In Ancient History

Mathematics is full of discoveries as found by scholars or mathematicians throughout history. All of these discoveries have allowed us to progress with arithmetic algebra calculus and to develop a theorem to empower new ideas.

In the 5th century zero emerged as a number in its own right. Hindus from India invented zero to represent the idea of the power of the cosmos and universe as they expand into infinity. They called this the sunya which means empty in Sanskrit.

The book Brahma Sphuta Siddhanta was published in c. 628 by Brahmagupta which defines zero as the subtraction of a number by itself, e.g. 5-5 =0. Here is where the journey of zero begins, in India as a concept of nothingness.

In the west, the number zero has negative connotations, you might call someone a zero to mean that they are a loser. But in India, Buddhists and Hindus understand the concept of nothingness to be the attainment of nirvana. This might be why the idea of zero came so naturally to them because this concept is central to their beliefs and further it is something that they are trying to attain.

zero has many other meanings and representations Renewal or a new beginning, to “start from scratch” and to “reset.”Photo Source: Unsplash

Experiments With Zero

In further peer-reviewed experiments, they also discovered that the mathematical model of zero is immune to division, multiplication, adding and subtracting. When the number is estimated to try to get a result, the answer will always move further away from the number. Try it 1 / 0.0001 = 10,000 (what?? How!!)

Logic games like this taught them and us that zero is bound to the infinite or undefined since zero divided by anything is zero. The fraction 1/0 was born and in attempting to solve it and exploring the infinite at a deeper level decimals were created.

The International Zero

In the 7th century with the expansion of the Arab culture in the Muslim world. Zero is adopted from the Hindus as a representation of emptiness and infinity. They use the word sifr which means zero in Arabic.

In the 12th century, the zero pops up in Europe and along with that so does Arabic mathematics. But the Catholic church is reluctant and suspicious of the idea of being able to physically write or describe something that means the void, null or the infinite.

In 1200, Leonardo Fibonacci, an Italian mathematician, adopts the Arabic word sifr and translates it into Latin. “zephirum”, gradually becomes “zephiro”, “zeuero”, “cero” (Spanish) and finally, “zero” (Italian) and “zero” in English.

Zero The Evil Number?

Although zero had been prohibited by the churches, they believed zero and the representation of nothingness to be the incarnation of the devil. However, it spread like wildfire through the streets and merchants used it along with decimal numbers.

Maths Worldwide

Liber Abaci, a book on arithmetic is published by Fibonacci who had travelled across Africa, the Middle East, Greece and Egypt to collate all of the mathematical knowledge of the period. These included math concepts and math facts, it was one of the well-recorded textbooks of the era on core standards of maths internationally.

The Different Meanings Of Zero

Zero is not just the point between positive numbers and negative numbers or just the absence of quantity. It is a mathematical symbol which has a philosophical, religious and cultural background.

Indeed it a simple ‘0’ has meant many things to many people including the devil, chaos, emptiness, infinity and nothingness. Today it also represents something free (£0), Infinitesimal (0.00001) or Null (0). It represents the starting point of things or the pause before things begin. Its also symbolism for unity and eternity, the closed circle. However, its links to infinity are separated from the ‘8’ symbol just by the idea that it has so many other meanings and representations.

Here are other meanings attributed to zero:

  1. Renewal or a new beginning, to “start from scratch” and to “reset.”
  2. Security is inferred by it’s round and closed shape,
  3. The idea of fertility, femininity and the fetus can be found in the circle
  4. Perfection in its shape as each edge is linked to its centre.
  5. The cycle and regeneration, as the outer edge of zero, leads back to itself.

Zero As Found In Common Expressions:

As we have discovered zero is not just a number used to solve math problems or expand your math skills. While it did begin in many cultures as just a number in basic math and algebra. The idea of zero has also permeated common core sayings in English and other languages worldwide.

Expression using the words zero refer to the state of something being missed, missing, non-existent, absent or restarting.

Common Expressions:

  1. A circle of friends (the unit),
  2. A vicious cycle, (restarting)
  3. Have a zero point (bottom),
  4. Start all over again (reset)
  5. Start again from the beginning, (reset)
  6. Zero tolerance,
  7. Have zero driving skills, (absence)
  8. zero in my Account, (number)
  1. A lot of fuss about nothing (absence)
  2. A blank slate (reset) such as telling time (00:00)

discoveries have allowed us to progress Mathematics is full of discoveries as found by scholars or mathematicians. Photo Source: Unsplash

Some Mathematical Properties Of Zero

Revising mathematics is impossible without the zero, it is essential in math in either its presence or its concept. But zero in math is not always as apparent as it seems and it can be at the root of some cool math games which can make learning maths much more fun than generally assumed.

Zeros importance in maths is due to it position between the negative numbers and positives numbers( -1, 0, 1), as a number itself (0) and as a marker of the absence of other numbers (10). For such a simple symbol It is very accomplished and has had centuries to develop itself into the position that it holds today.

  1. It is the smallest natural whole number,
  2. and it is also a neutral element,
  3. it is the only number to be both positive and negative at the same time.
  4. This is the only number that remains unchanged when subtracted or when added to another number (1 + 0 = 1 or 1 – 0 = 1)
  5. In the multiplication tables, zero is the only number which, when multiplied by any other number, returns the result to a zero quantity.

Different Ways To Learn Maths

There are a considerable number of ways to learn more about the power of zero and to learn mathematics as a whole. You can try online classes, number patterns, a math game app, games for kids, math videos and even private math lessons.

Designing your study program to split up the math that you are having trouble with will make it easier to remember. You can use math worksheets, get creative and use your own number system, do some puzzles, quizzes, learn fun math facts, practice your equation notation…etc.

Coolmath Ideas To Reinforce Math Learning

  • Interactive math: Go to online math websites and download printable worksheets
  • Learn number patterns with fun number lines
  • Grade Math: Find easy to hard games for kids online by grade level
  • Call it by another name Differential equations to DE and Trigonometric functions to Trig F. it even sounds like cool math and certainly less intimidating.
  • Play cool math games like sudoku
  • Attend free math study groups
  • Mathematics courses: Take specialist math courses privately so you can spend more time understanding the concept
  • Test your basic number sense hasn’t gotten rusty as it is the foundation for all other math. Common core standards like; basic Systems of equations, Multiplication and division, Addition and subtraction, Rounding, Pre algebra, precalculus, Geometric triangles and other Mathematical concepts.
  • Math online: Watch math videos, great math practice for solving problems
  • Ask your math teacher for the core standards to pass the class and ask for math help specifically for the part you are struggling with.
  • Hire a tutor for math tutorials: while you normally have to pay for tutoring you can often find free online math tutors especially If you can offer to exchange the teaching math or math help with something that they want to learn. It’s a free way to work with a math tutor.

As a learner, you must learn to recognise how you prefer to learn and which methods give you the best results. High school math, college math and onwards is challenging, it is not basic math like counting, multiplying, dividing, adding or subtraction. The more you the practice the higher the Probability that you will achieve mastery in your mathematics education and curriculum.

Read more about the other special numbers; Pi or Archimedes constantthe golden ratio or divine proportion, the important prime numbers, and the rare perfect numbers.


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