Early Life
Where was Johann Bernoulli born and when? (Country, city, year) Bonus 50 points: provide his birth Month and Date.
Switzerland, Basel, 1667, August 6th
Johann Bernoulli came from a family of well-known mathematicians. Who is the brother of Johann Bernoulli?
Jakob Bernoulli
Johann Bernoulli raised the famous "brachistochrone problem" (lit. shortest time problem). Which year was the problem posed in?
1696
What was the most bitter dispute between Johann and his brother? Who won this dispute?
His brother ultimately solved the isoperimetric problem. He provided the proof showing that, among all closed curves of a given length, the circle is the shape which encloses the maximum area.
Before becoming a mathematician, which field of study did Johann Bernoulli pursue?
Bernoulli studied medicine.
In 1692, Johann Bernoulli began tutoring this mathematician. This mathematician will later publish the first differential calculus textbook. Who is this mathematician?
Marquis Guillaume-François-Antoine de L'Hospital
In 1690 Bernoulli became the first to use the term ‘integral’ in analyzing a curve of descent. A year later his study of catenary(the curve formed by a chain suspended between its two extremities) was applied in what area?
The building of suspension bridges. In 1695 he also applied calculus in designing bridges.
Who did Johann Bernoulli marry and what year? Who are his wife’s parents?
He married Dorothea Falkner in 1694. The daughter of Daniel Falkner and Anna Catharina König.
In 1695, Johann Bernoulli became a professor of mathematics at this Dutch university.
The University of Groningen
Johann Bernoulli is said to have developed a theorem that can be used to take the limit of a function in its indeterminate form. What is the name of this theorem?
Bernoulli's rule or L'Hôpital's rule
Johann liked to solve problems in physics and engineering. Give an example of his works in this field.
The theory of fluid dynamics, the principle of virtual work in mechanics, etc.
Bernoulli raised the famous "brachistochrone problem". What is the problem about?
Finding the curve of the quickest descent of an object between two points at different altitudes, where the two points are not along a vertical line.
Where did Johann Bernoulli receive his most advanced degree and which year did he receive this degree? What was his thesis on?
Bernoulli received his MD degree at the University of Basel in 1694 with a thesis on muscular contraction.
According to Johann Bernoulli, who discovered calculus?
Leibniz
What was Johann's first major publication related to calculus? What was it about?
"Problema novum ad cujus solutionem mathematici invitantur". It was about the Brachistochrone Problem.
What is the solution to the "brachistochrone problem"?
Cycloid curve (The path along which a bead sliding without friction under the influence of gravity will reach the bottom in the shortest time possible from any point. He discovered this solution through the method of variations.)
Johann Bernoulli's father initially wanted him to pursue this career. Bonus 50 points: Why?
Business. Because his father had a family spice business.
In 1691, Johann Bernoulli became famous among France's elite scientists and philosophers for his development of a formula. However, this formula was actually discovered by someone else. What was this formula used for and who actually developed this formula?
It was the formula for radius of curvature of a curve and it was first given by Jakob Bernoulli.
One of the theorems developed by Johann Bernoulli is widely known as the L'Hopital Rule. Why was the theorem not named after Bernoulli?
Johann sold it, along with a number of his mathematical discoveries to Marquis de L'Hospital, who was his employer at the time. L’Hospital eventually published the theorem in his textbook “Analyse des infiniment petits (1696)".
The Bernoulli's principle, which states that the pressure in a fluid decreases as its velocity increases, was stated by Daniel Bernoulli. What is the relationship between Daniel Bernoulli and Johann Bernoulli? (Precise answer required)
Daniel Bernoulli was Johann Bernoulli's second son.