1. Special Numbers

2. Zero
The 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

3. 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

4. Who Accepted Zero?
Egyptians developed a symbol for zero around 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

5. 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

6. Map and timeline of zero

7. Pi
The 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

8. What is it? Pi is a Greek Letter
It represents the ratio of the circumference to the diameter
𝜋= 𝐶 𝑑
Where C is the circumference of the circle and d is the diameter of the circle
From this we get the formula for Circumference

9. Who had it? Babylonians: approximately 25 8
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 (averaging these gets us )
Ptolemy: had the value of ≈
Ch’ang Hong calculated: 𝜋= ≈3.162
Tsu Ch’ung-chih and Tsu Keng-chih calculated: 𝜋 = ≈
A more accurate value would not be found for 1,000 years

10. 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

11. 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.

12. 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

13. 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

14. 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”

15. 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.”

16. Negative numbers
I tried really hard to find a quote about negative numbers, but apparently none exist.
- Miss Ord

17. 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

18. 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

19. 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