Who Discovered Zero?

By: Claire Kazen

May 25, 2007

Focus Of Presentation

The History of Zero Before Zero Birth of Zero

Zero in the classroom How zero needs to be emphasized more Meaningful activities to explore zero

First Things First

Two uses for zero, both extremely important One

Empty place indicator • 2106 clearly different from 216

Two The number itself

• Zero, derives from the Arabic sifr

Life Without Zero

Can you imagine mathematics without zero? Numbers were used to count creatures or

objects 40 cows in the field Six loaves of bread at the marketplace

Counting zero sheep or loaves of bread did make much sense

Zero was just not needed!

Before Zero

Numbers were used for thousands of years before they used zero

Historical records show different path towards the concept Zero made appearances only to vanish again Mathematicians were searching for it yet did

not recognize its fundamental significance

Egyptians

Egyptian hieroglyphics were used as early as 3500 B.C.E.

Egypt did not have~ or need~ a zero.

Even without zero, Egyptians became masters of mathematics.

Greeks

The Greeks brought mathematics to its highest point in ancient times.

Around 500 BC, the Greeks developed a newer more sophisticated system This way avoided repeated letters

Romans

The Romans also had a number system It was a step back from

the less sophisticated Egyptian system.

The Roman 87, LXXXVII, requires seven symbols, with several repeats

Still…

The Egyptian, Greek and Roman number systems still had no zeros

Even though the Greek number system was more sophisticated than the Egyptian and Greek, it was not the most advanced.

Babylonians

2500 B.C.E., the Babylonians used a system of two symbols Base 60

They sometimes used a space to represent an empty position.

By about 200 C.E., they used a pair of small triangles to represent an empty position.

Babylonians never actually invented a zero, they made an important first step!

Babylonians

India

Hindu culture had a positional number system in base ten They used a dot to represent an empty place

Sunya which meant “empty” was the name for this dot

At this point, the early zero was a placeholder and an aid in computation

By 500 C.E., the Hindus use a small circle to represent Zero! This circle was recognized as a numeral

Hindu- Arabic Numerals

Arabic people recognized the value of the Hindu system They adapted the numerals and computation Then spread the ideas in their travels

The zero was named with the Arabic word sifz The actual word “zero” came from Italy

Spreading The News

Leonardo of Pisa, known as Fibonacci Born to a merchant

family living in North Africa

Learned Hindu-Arabic numerals from his Arabic tutors

He brought the news of zero and new computational methods to Europe in his book

Fear of Zero!

Europeans resisted Hindu-Arabic numerals

It seemed strange The numerals, including zero, were not

accepted Florence, Italy, passed a law prohibiting the use

of the numerals 0 could be changed to look like 6 or 9

Slowly, the numbers became accepted 1500s

Birth of Zero

In the history of culture the discovery of zero will always stand out as one of the greatest single achievements of the human race.

-Tobias Danzig

Without zero we would lack Calculus, financial

accounting, the ability to make arithmetic computations quickly and computers!

Zero Is A Special Number

If we add 0 to any number, the sum is the original number Same is true for subtraction

If you multiply any number by 0, the product is 0 If you raise any nonzero number to the power of 0, the

resulting number is 1 If you divide 0 by any nonzero, the quotient is 0 Any number divided by 0 is undefined

Zero is…..

It is the number that separates positive numbers from negative numbers

It is even It is the integer that precedes one Zero must sit in its rightful place on the

number line, before on and after negative one

BUT….

Yet zero sits at the end of the computer key board and at the bottom of the telephone!

Because we always start counting with one!

Difficulties With Zero

Writing numbers 100, 110, and 101 Older children

Only 50% of seven grader could correctly write “two hundred thousand and forty-three”

Addition and Subtraction problems 2000-169

Multiplication and division problems 0x6 and 6/0 Also 9x306

Comparing decimal fractions 0.02 and 0.002 or 0.2 and 0.20

How As Teacher We Can Help

Zero is an important number and it does in fact “do something”!

Zero needs to be introduced in early education Zero is sometimes overlooked when

introducing numbers

With older grades, make sure to have problems with zero

Meaningful Activities with Zero

Discuss the use and verbalization of zero Street addresses, telephone and PIN numbers

Name things that there are zero of in the classroom

Put a coin in all but one container; shut them and ask the children to guess which one has zero coins

Include a blank card in sorting exercises

More Activities

Explore number patterns involving addition, subtraction, multiplication, and division of zero

Exploration of true/false statements 10+0=10, 100-120=0, and 4+0>4

Story problems “There are 0 grams of fat in each serving of

cucumber. How many grams of fat are in 7 servings of cucumber?”

Resources Anthony, Glenda, and Margaret Walshaw. “Zero: A “None”

Number?” Teaching Children Mathematics. August 2004

Humes, Alexander. Zero to Lazy Eight, The Romance of Numbers. Simon and Shuster. New York, New York, 1993.

Ifrah, Grorges. The Universal History of Numbers. John Wiley and sons, Inc. New York, New York, 2006.

O’Connor, JJ and E F Robertson. “History Topic: A history of Zero,” MacTutor History of Mathematics. Noverber 2000. http://www-history.mcs.st-andrews.ac.uk/HistTopics/Zero.html

Resources

Seife, Charles. Zero: The Biography of a Dangerous Idea. Penguin Group Penugin Putnam Inc. New York, New York, 2000.

Wallin, Nils-Bertil. “The History of Zero, How was Zero Discovered?” Yale Global, 19 November, 2002.

Wilson, Patricia S. “Zero: A Special Case.” Mathematics Teaching in the Middle School. 6 no 5 300-3, 308-9 Jan 2001.

“O” Wikipedia, May 2007. http://en.wikipedia.org/wiki/0_%28number%29