 # Leonhard Euler: The Basel Problem

Good Essays
904 Words Grammar Plagiarism  Writing  Score Leonhard Euler: The Basel Problem By: Victor Hui

Introduction
Leonhard Euler was a ground-breaking Swiss mathematician and physicist from the 1700's. He made many revolutionary discoveries. However, the one that caught my eye was his solution to the Basel Problem in the year 1734.
The Basel problem was initially posed by an Italian mathematician by the name of Pietro Mengoli in the early 1640's. This problem baffled the even the greatest minds at the time. Branching from mathematical analysis, the Basel problem involved knowledge of convergent series. Convergent series are series where the sum of all terms approaches a limit. As a result of solving a problem that tormented even the brightest mathematicians of the time, Leonhard Euler's and his Solution became exceedingly
Through the Basel Problem's definition, Bernhard Riemann produced a mathematical notion which is identical to the Basel Problem except for the fact that rather than the reciprocal squared, we have the variable "s".
The Riemann created a function in which currently states that any value of "s" that makes the series equate to zero is either a negative even integer (trivial zeros) or when the horizontal axis equates to 1/2 (called the critical line). The critical line lays in between the horizontal axis equating from 0 to 1. We call this the critical zone. The Riemann Hypothesis asks for a nontrivial zero from the critical zone, a value of "s" that makes the function equate to zero that is not a negative even integer or does not lie on the critical line. This hypothesis was marked as one of the millennium problems. No one has been able to find non trivial zeros off of the critical line and inside of the critical zone. The rules of the millennium problems states that one million dollars is awarded to the mathematician that can find a zero outside of the critical line and inside the critical

## You May Also Find These Documents Helpful

• Good Essays

In 50 A.D., Heron of Alexandria studied the volume of an impossible part of a pyramid. He had to find √(81-114) which, back then, was insolvable. Heron soon gave up. For a very long time, negative radicals were simply deemed “impossible”. In the 1500’s, some speculation began to arise again over the square root of negative numbers. Formulas for solving 3rd and 4th degree polynomial equations were discovered and people realized that some work with square roots of negative numbers would occasionally be required. Naturally, they didn’t want to work with that, so they usually didn’t. Finally, in 1545, the first major work with imaginary numbers occurred.…

• 641 Words
• 3 Pages
Good Essays
• Good Essays

Jons Jacob Berzelius (1779 - 1848) - He was Swedish and gave the technique of chemical formula notations. He also proposed the law of constant proportions, which proved that inorganic substances are made of elements that are in constant proportion by weight.…

• 482 Words
• 2 Pages
Good Essays
• Good Essays

In AD 499 the Indian mathematician Aryabhata used the notion of infinitesimals and expressed an astronomical problem in the form of a basic differential equation. This equation eventually led Bhāskara II in the 12th century to develop an early derivative representing infinitesimal change, and he described an early form of "Rolle's theorem". Around AD 1000, the Islamic mathematician Ibn al-Haytham (Alhazen) was the first to derive the formula for the sum of the fourth powers, and using mathematical induction, he developed a method that is readily generalizable to finding the formula for the sum of any integral powers, which was fundamental to the development of integral calculus. In the 12th century, the Persian mathematician Sharaf al-Din al-Tusi discovered the derivative of cubic polynomials, an important result in differential calculus. In the 14th century, Madhava of Sangamagrama, along with other mathematician-astronomers…

• 1190 Words
• 5 Pages
Good Essays
• Good Essays

The first man who was credit for major contribution was French mathematician Joseph Fourier, on the idea of physical laws for instance F=ma.…

• 770 Words
• 4 Pages
Good Essays
• Satisfactory Essays

Leonhard Euler (15 April, 1707- 18 September, 1783) was a Swiss mathematician and physicist. Born in Basel Switzerland, later moved to neighboring town, Riehen, Euler attended a rather poor school that taught no mathematics. His father having studied theology at the University of Basil managed to teach him some, which ignited an interest in Euler for the subject and at just 14, he began attending the University of Basil studying philosophy and theology. He completed these studies in 1726. Leonhard Euler: The first St Petersburg years by R. Calinger summarizes this time period flawlessly. “... after 1730 he carried out state projects dealing with cartography, science education, magnetism, fire engines, machines, and ship building. ... The core of his research program was now set in place: number theory; infinitary analysis including its emerging branches, differential equations and the calculus of variations; and rational mechanics. He viewed these three fields as intimately interconnected. Studies of number theory were vital to the foundations of calculus, and special functions and differential equations were essential to rational mechanics, which supplied concrete problems.” However, the publication of his book Mechanica in 1736 was the beginning of Euler’s major mathematical discoveries.…

• 444 Words
• 2 Pages
Satisfactory Essays
• Satisfactory Essays

* Archimedes-One of the major contributions Archimedes made to mathematics was his method for approximating the value of pi. It had long been recognized that the ratio of the circumference of a circle to its diameter was constant, and a number of approximations had been given up to that point in time. Archimedes was the first person to calculate the value of pi.…

• 364 Words
• 2 Pages
Satisfactory Essays
• Good Essays

Isaac Newton and Gottfried Leibniz introduced Calculus to the world. It is the math of motion and change, and as such, its invention required the creation of a new mathematical system, hence it is broadly used in all fields of engineering, sports, biology, economics, medicine etc. Also its just generally useful in life excluding academics.…

• 717 Words
• 3 Pages
Good Essays
• Good Essays

One of his most important and interesting discoveries is probably what is known as the Fibonacci sequence. It goes like this: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. He discovered this sequence through an experiment on an over population and breeding of rabbits. He then realized that if you add the last two numbers together you get the next one.…

• 462 Words
• 2 Pages
Good Essays
• Good Essays

Leonhard Euler was considered of the greatest mathematicians that ever existed. He was responsible for creating many math concepts including the invention of i. He also wrote many books that are still used to this day to teach students all over the world.…

• 518 Words
• 3 Pages
Good Essays
• Good Essays

A well know problem that the brothers applied themselves to was the designing of a sloping ramp that would let a ball roll from top to bottom at the fastest possible speed. Johann demonstrated through calculus that neither a straight slope nor one with a very steep initial slope was the right answer. The answer was a curve with a less steep initial slope that was more optimal called a brachistochrone curve which is like an upside down cycloid. This is the perfect example of ‘the Calculus of Variations’ generalization that they developed together. This idea has been largely used in a number of fields such as engineering, financial investment, architecture and construction even space travel.…

• 657 Words
• 3 Pages
Good Essays
• Better Essays

was not at all happy about this idea but he lacked the courage to stand up to…

• 2131 Words
• 9 Pages
Better Essays
• Good Essays

Gottfried Wilhelm von Leibniz was born in 1646 to Catharina Schmuck, an extremely religious being, and Friedrich Leibniz, a moral philosophy professor at Leipzig. Gottfried grew up with a religious and moral value set environment. Those values were an important contribution to Gottfried’s philosophy and life in the future. Leibniz was a German philosopher and mathematician. With Leibniz’s ideas and theories, he became a prominent figure in mathematics and was a major mathematician that greatly contributed to calculus.…

• 624 Words
• 2 Pages
Good Essays
• Powerful Essays

Most examples or evidence we have of these types of problems were used in their own real world, concrete problems such as, the weight of a stone or how to break up a piece of land among 3 pairs of brothers (Corry, 2005). Although, the Babylonians could find a solution to a general quadratic or linear equation, the solution to a simple cubic equation or even square root equation was not in their realm (Jordman, 2009). In fact, the computations of many problems included some unknown number because the number zero, negative numbers and irrational numbers were not a part of their number system (Kleiner, 2007).…

• 1448 Words
• 6 Pages
Powerful Essays
• Good Essays

By proving this, Euler showed that there is some relation between the prime numbers and the RZF. The relation remained unknown until when Riemann expanded the range of s. Euler had only worked with real values of s and Riemann was the ﬁrst to open up the function to the complex plane where s = σ + ıt (1.3)…

• 4599 Words
• 19 Pages
Good Essays
• Good Essays

Archimedes produced the first known summation of an infinite series with a method that is still used in the area of calculus today.…

• 1058 Words
• 5 Pages
Good Essays