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BIBLIOGRAPHY
https://thescienceclassroom.wikispaces.com/Leonhard+Euler#Leonhard%20Euler-Major%20Contributions
http://www.thefamouspeople.com/profiles/leonhard-euler-biography-441.php
https://en.wikipedia.org/wiki/Contributions_of_Leonhard_Euler_to_mathematics
http://www.famousscientists.org/leonhard-euler/
http://www.biography.com/people/leonhard-euler-21342391
https://www.mathsisfun.com/geometry/vertices-faces-edges.html
https://en.wikipedia.org/wiki/Basel_problem
http://mathworld.wolfram.com/EulerFormula.html
https://www.mathsisfun.com/geometry/eulers-formula.html
His Contributions to other subjects
Thus his findings for the 3D shapes evolved he proved regular 3D object to the parabolic shapes. Evolving the formula from F+V-E=-2 and many more.
They use it to investigate what properties an individual object can have and to identify properties that all of them must have. Euler's formula can tell us, for example, that there is no simple polyhedron with exactly seven edges. You don't have to sit down with cardboard, scissors and glue to find this out — the formula is all you need. The argument showing that there is no seven-edged polyhedron is quite simple, so have a look at it if you're interested.
Using Euler's formula in a similar way we can discover that there is no simple polyhedron with ten faces and seventeen vertices. The prism shown below, which has an octagon as its base, does have ten faces, but the number of vertices here is sixteen. The pyramid, which has a 9-sided base, also has ten faces, but has ten vertices. But Euler's formula tells us that no simple polyhedron has exactly ten faces and seventeen vertices.
Contributions to Mathematics
These contributions include the modification, creation, and the familiarization of common mathematical notations of today. His efforts helped spread mathematics over the world and stimulate the development of collaborative, problem solving. The discovery that earned Euler the most fame was the equation :
e^(ix)=cos x+ i sin x,
At about this time his work on exponential functions led him to introduce the constant e, the symbol for the important transcendental number 2.71828... . He also discovered the result
Further Contributions
Much of the notation used by mathematicians today - including e, i, f(x), ∑, and the use of a, b and c as constants and x, y and z as unknowns - was either created, popularized or standardized by Euler. His efforts to standardize these and other symbols (including π and the trigonometric functions) helped to internationalize mathematics and to encourage collaboration on problems.
Contributions to Mathematics
(Continued)
Leonhard Euler made significant contributions to calculus, modern geometry and trigonometry.
He made the formula f(x), where f is the function which relates to an input and output.
In 1736, using graph theory and topology, Euler solved a problem known as the seven bridges of Königsberg that was deemed unsolvable until then. He revolutionised the way we think of mathematics today.His work has been recorded in approximately 30 books which he wrote himself.
His academic mind continued as he proved many more formulas
Another formula is F + V − E = 2
Where F is = to how many faces is on a 3D object
V is= to how many vertices is on a 3D object
And E is =to how many edges
A mathematician who made a change to people perspectives , who made influential discoveries in many branches of mathematics like infinitesimal calculus , and pioneering contributions to several branches such as topology and analytic number theory.
~Group 3
Basel Problem
His Achievements
He solved the Basel problem in 1735, more accurate than even the Bernoullis could achieve (at the time, the Bernoulli's were a renowned family in mathematics). Daniel Bernoulli reached a conclusion of 1 and 3/5, whilst Eulers method produced him a rather unexpected, exact result/conclusion of pi 3/6.
*Also, as mentioned previously, he solved the problem of "seven bridges of Königsberg" which was deemed unsolvable until them.
*Euler wrote books which explained his theories.
*He developed formulas for many different subjects which would solve many problems later on.
After that..
The 1730's was a period of time, wherein many problems were solved by the world renowned Euler, including requests from the Russian Government himself.
*Euler's father wanted him to become a pastor, so Euler firstly studied theology, Greek and Hebrew. However, he soon realised that these subjects dd not interest him and therefore Euler chose mathematics because he was he had grit and compassion.
Later on
*Euler moved to Russia on the 17th of May 1727 to learn at the academy at Saint Petersburg. He was promoted to a position in the maths department there during his stay with Daniel, one of Johan Bernoulli's sons.
* They became suspicious of the foreign scientists in the academy, like Euler, so they cut the funding and caused other difficulties for the scientists. Eventually, conditions improved, and in 1731 Euler became a professor in physics.
*2 years later, Euler succeeded as head of the academy, and a year later, he married Katherina Gsell (1734). They had 13 children, of which only 5 survived from an unfortunate childhood.
Early Life
*Leonhard Euler was born on the 15th of April, 1707, in Basel, Switzerland. He had two sisters growing up. Euler's father was a pastor, and his mother was the daughter of a pastor, so Euler grew up with a religious background.
*His father, Paul Euler, taught him mathematics at a young age, so Leonhard would grow up with a lifelong love for maths thus developed his understanding of mathematics through the teaching ofJohan Bernoulli', a famous mathematician during the time.
*Soon later Euler pursuit his dream and career through the attendence atUniversity, and received a Master of Philosophy degree.