SPECIAL NUMBERS

ZEROThe point about zero is that we do not need to use it in the operations od daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.

- Alfred North Whitehead

FEAR OF ZERO

Most ancient people believe that only emptiness and chaos existed before the universe was created.

Emptiness and disorder were the orginal state of the cosmos

There was a fear that it would take over again at the end of time

Zero represented that void

WHO ACCEPTED ZERO?

Egyptians developed a symbol for zero around 1740 BC

- Accounting Texts and Measuring Babylonians needed a place holder, but zero

didn’t seem to be a number in its own right Maya had a symbol for zero The Western World rejected zero for nearly 2

millennia The Greeks specialized in Geometry and had

no real need for zero - The lack of zero stunted the growth of

both mathematics and science

WHERE THE WORD CAME FROM

Sanskrit: shoonya or sunya meaning empty Arabic: sifr meaning “it was empty” or

“nothing” It evolved to cifra and zefirum 14th Century France: chiffre Italy had 3 versions: zefiro, zevero, and zero 15th Century Germany: ziffer France and England: zero

MAP AND TIMELINE OF ZERO

PIThe value of π has engaged the attention of many mathematicians and calculators from the time of Archimedes to the present day, and has been computed from so many different formulae, that a complete account of its calculation would almost amount to a history of mathematicts.

- James Glaisher

WHAT IS IT?

Pi is a Greek Letter It represents the ratio of the circumference to

the diameter

Where C is the circumference of the circle and d is the diameter of the circle

From this we get the formula for Circumference

WHO HAD IT?

Babylonians: approximately Egyptians: approximately Archimedes: using two polygons with 96

sides each and using the perimeter arrived at decision that it was less than but greater than 3 (averaging these gets us 3.1419)

Ptolemy: had the value of Ch’ang Hong calculated: Tsu Ch’ung-chih and Tsu Keng-chih

calculated: A more accurate value would not be found

for 1,000 years

INFINITE SERIES

Used by mathematicians such as Madhava of Sangamagrama, Isaac Newton, Leonhard Euler, Carl Friedrich Gauss, and Srinivasa Ramanujan

Simple infinite series for pi is the Gregory-Leibniz, sometimes called the Madhava-Leibniz series

INFINITY In ordinary conversation, infinite means something that is very great in comparison with every day things. In mathematics, however, infinity is not a number but a concept of increase beyond bounds.

BASICS OF INFINITY

Infinity comes from the Latin word infinitas, which can be translated as “unboundedness

That came from the Greek words apeiros, meaning “endless”

Infinity isn’t a specific number, its an idea Infinity was about as popular as 0 in the

beginning Eventually it became a philosophical concept

ACCEPTANCE

Anaximander (a Greek Philosopher) used the word apeiron which means infinite or limitless

- This is the earliest recorded idea of infinity Zeno of Elea had the earliest conclusive use

for mathematical purposes The Hindu had references as early as 500 BC Now it is accepted to mean not finite in

mathematics

GEORG CANTOR

Defined two different types of infinity - Countably infinite and Uncountably infinite

His theories at the time were referred to as a “grave disease” entering into the discipline of mathematics

One mathematician called his theories “utter nonsense”, “laughable” and “wrong”

Cantor himself was referred to as “a scientific charlatan” and a “corrupter of youth”

GEORG CANTOR NOW

Today we know better In 1904 he was awarded the Sylvester Medal

by the Royal Society (the highest honor it can confer for work in mathematics)

Mathematician David Hilbert stated: “No one shall expel us from the Paradise that Cantor has created.”

NEGATIVE NUMBERS I tried really hard to find a quote about negative numbers, but apparently none exist.

- Miss Ord

CHINA

Negative numbers first appear in “Nine Chapters” in China

Positive numbers were in red and negative numbers were in black

A money balance was positive, and a deficit negative

GREECE AND THE REST OF EUROPE

Diophantus (an Alexandrian mathematician) called negative results “absurd”

European mathematicians resisted until the 17th century

Fibonacci only allowed for negative results when they could be interpreted as debits and losses

Francis Maseres wrote that negative numbers “darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple.”

In the 18th century it was common practice to ignore negative results

INDIA

Appeared about 620 AD in the work of Brahmagupta

Fortunes were positive and debts were negative

He even had rules for dealing with these numbers