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- History of Mathematics

Ray C.

Who was responsible for the earliest known form of written mathematics?

The Babylonians (2000 - 1500 BC).

In what era was the Pythagorean theorem born? What does it tell us?

The Pythagorean theorem was introduced in Ancient Greece. It tells us that the hypotenuse of a right-handed triangle is equal to the sum of the squares of the two remaining sides.

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What concepts from Arabic mathematics are still around?

- Zero
- Algebra
- Algorithm
- Arabic numerals (0, 1 ,2 ...)

What is linear perspective?

Linear perspective was re-discovered by Filippo Brunelleschi during the Renaissance. It is a way of creating a convincing, perfect illusion of space on a flat, or two-dimensional surface.

How does linear perspective work?

Parallel lines should converge towards a vanishing point and the size of an object should very inversely from the distance from the plane.

Who was the first computer programmer?

Ada Lovelace wrote conceptual programs for Charles Babbage Difference Engine.

Who was responsible for work in deciding which programs could be computed?

Alan Turing.

How did Pythagoras contribute to music?

Pythagoras investigated the relationship between musical notes by hitting bells of different sized or glass filled with varying amounts of water. Perhaps also the basis for interest in rational numbers (or harmonics).

Who's work was fundamental in the analysis of sound waves at a particular frequency?

Fourier.

What did the Babylonians contribute to maths?

- Algebraic problems

What are some computational devices?

- Abacus
- Calculating machine
- Analytical engine

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What is a Turing test?

A Turing test describes a machines ability to exhibit intelligent behavior. A judge speaks to two contestants for set amount of time, one a computer the other a human. If the two are indistinguishable, the machine has passed the test.

What did the Renaissance bring to mathematical thought?

- Links between science and art
- Parallel lines
- Vanishing points

Who investigated the relationships between rational numbers?

The ancient Greeks.

What was Iannis Xenakis interests?

- Structures in space and time
- Architecture and Music
- Metastasis

Who invented the base logarithm symbol 'e'?

Nicholas Mercator in 1965.

Who invented the integral symbol ∫?

Leibniz (17th century)

Who invented the square root symbol?

Christoph Rudolf (1525)

Who invented the infinity symbol ∞?

John Wallis (1655)

What human needs first inspired mathematics?

- Counting (stocks)
- Calculation (trade)
- Measurement (building)

What main topics came out of ancient mathematics?

- Geometry
- Algebra
- Number theory

What did Brunelleschi discover about vanishing points?

- Using mirrors, he rediscovered that all parallel lines of plane should converge towards a vanishing point.
- Calculated the distances at which objects should be drawn to accurately be represented in the picture.

Other than art, what else interested Brunelleschi?

- Mechanical devices
- Engineering

What did Dürer believe about new art?

What is unique about the Melancholia of Durer?

It contains the first magic square to be seen in Europe.

What did Dürer publish?

The first maths book in German.

In what work of Dürer can the perspective machine be seen?

Draughtsman Making a Perspective Drawing of a Woman.

What is an astrolabe?

An astrolabe is a navigational tool used for measuring latitudes at sea.

What did Leibniz say about reasoning and computation?

- Controversies could be resolved
- Men could calculate
- Speaking of reasoning devices

On what machine did Ada Lovelace work?

The Analytical engine of Charles Babbage.

What was the Analytical Engine?

A design for a general purpose store program computer.

What are the four schools of Pythagorean thought?

- Geometry
- Arithmetic
- Music
- Astronomy

How did Pythagoras discover musical notes/pitches?

By experimenting with cups, bells and pipes of different sizes.

What is the Loebner Prize?

Loebner Prize is a yearly award for AI agents that can pass the Turing test.

What was the name of the building Iannis Xenakis created at the same time as Metastasis?

Le Corbusier for the Philips Pavilion in the World Fair in Brussels in 1958

How did John Cage rely on chance?

He primarily took influence from the Chinese book 'I Ching' or 'The book of changes'.

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