Javier A. Tabush

Taming the infinite, a book about numbers and the history of mathematics. It was written by Ian Stuart.



Euclid of Alexandria

- Famous for his book about his elements.

 

Eternal Triangles
Trigonometry = measuring triangles, but it is actually useful for all mathematics. 

Origins of trigonometry:
The basic problems were the calculation and properties of a triangle (sides and angles). Trigonometry relies on a number of special functions (cosine, sine and tangent started by George Joachim Rhaeticus). It seems to have originated in astronomy using angles to measure distances. 
The most important book in trigonometry was Mathematical Syntaxis of Ptolemy. Early trigonometric was used by Hindu astronomers and mathematics. 

Some of the most important functions in mathematics:

• The logarithm (Log x, logxy =logx + logy)
• Nasperian logarithms
• Base 10 logarithms
• Number e

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Curves and Coordinates
 

 

 

Fermat: Discovered the connection between algebra and geometry. He was the first person to describe coordinates. 

Descartes: He gave us the modern notion of coordinates, and also the second and third dimension. 

One of the important applications of coordinates in mathematics are that they help us represent functions graphically. 
 

 

 

Calculus was invented by Isaac Newton. After its discovery, mathematical patterns governed almost everything in the physical world.

Calculus is the mathematics of instantaneous rates of change – how rapidly is some particular quantity changing at this very instant?

Calculus is divided into:

 

 

 

Differential Calculus:

Rates of change

Geometric application: tangents to curves, derivative of a function.

Derivative of a function: the rate at which  f(x) is changing compared to how x is changing (the rate of change of f (x) with respect to x.

F( x + h ) – f (x) / h

Integral calculus:

Given the rate of change of some quantity, it specifies the quantity itself.

Geometric application: computation of areas and volumes.

Reverse process of derivation.

∫ g (x) dx

 

Physical astronomical background:

 

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• Planets: From Ptolemy, to Copernicus, to Brahe, to Kepler, to Galileo. 

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• Kepler´s laws of planetary motions that are still in use today:

1.  

1.     Planets move around the sun in elliptical orbits. 
2.  

1.     Planets sweep out equal areas in equal times. 
2.  

1.    The square of the period of revolution of any planet is proportional to the cube of its average distance from the sun

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