In mathematics, the notion of number has been extended over the centuries to include 0, negative numbers, rational numbers such as 1/2
and −2/3, real numbers such as √2 and π, and complex numbers, which extend the real numbers with √−1.
A number is a count or measurement. It is really an idea in our minds.
○ count: the total determined by counting
○ measurement: the size, length or amount of something, as established by measuring
BC 0800? Roman Numerals
The Romans showed numbers into the thousands using these 7 symbols: I for 1, V for 5, X for 10, L for 50, C for 100, D for 500 and M for 1000.
BC 0570 - 0495 Pythagoras
○ How many ways are there to prove the Pythagorean theorem? - Betty Fei
○ James Garfeild, Pythagoras, hypotenuse, tessellation, Euclid
BC 0500? Pythagorean Mathematicians
Their dictum of "All is number" suggested that numbers were the building blocks of the Universe and part of this belief was that everything from cosmology and metaphysics to music and morals followed eternal rules describable as ratios of numbers.
BC 0500? Hippasus
According to Pythagoras theorem the diagonal length of a square with each side measuring one unit would be square root of two.
The assumption that square root of two could be expressed as a ratio of two integers deduces a contradiction.
BC 0500? Hippasus
Some quantities, like the diagonal of a square with sides of length 1 couldn't be expressed with any combination of whole numbers or fractions, no matter how small.
BC 0300? Euclid
It was the Greek mathematician Euclid who produced the first precise description of the golden section.
A length is devided into two parts in such a way that the smaller part is to the larger part in the same proportion as the larger one is to the whole.
0750± positional notation
By the 8th century, Indian mathematicians had perfected positional notation and over the next several centuries, Arab merchants, scholars and conquerors began to spread it into Europe.
○ vigesimal, Maghreb, Hebrew, glyph, Aztecs, duodecimal, sexigesimal
1202 Leonardo Fibonacci
Fibonacci asked himself how many pairs of rabbits originated from a single pair in one year. Each pair of rabbits will produce exactly one more pair of both sexes per month which in turn would be fertile from the second month after birth.
1571 - 1630 Johannes Kepler
Keplar observed that the relationship between a number in Fibonacci sequence and the previous number more and more closely approaches the irrational number Φ the longer the sequence is continued and Φ describes nothing other than the golden section.
1643 - 1727 Isaac Newton
Galileo had already discovered some years prior that the distance traveled by a falling object is represented by a function of time.
Newton wondered how one could calculate the velocity of the object at any particular instance during the fall.
cardinal, ordinal and nominal number
A cardinal number says how many of something there are. An ordinal number tells the position of something in a list. A nominal number is a number used like a name.
The number of dimensions is how many values are needed to locate points on a shape.
Expansion of Numbers and Operations