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John Napier comes close to discovering number e.
John Napier invents what he called logarithms to multiply large numbers together. The idea is that if two numbers could be written as the same base then we could multiply them together by adding their exponents instead. His equation can be written as N=10^(7)(1-106(-7))^(L). By simplifying the equation you would find that Napier used a base very near to 1/e. With this being said this was just by accident and did not show that he knew anything about the existence of e (Maor, 1994, p. 7-9). -
Gregoire de St. Vincent finds that the area under y=1/x is related to logarithmic function.
St. Vincent discovers y=1/x from a number greater than zero to a number t grows geometrically while corresponding areas of rectangles associated with the area grow arithmetically. This showed that the relation to the area and distance along 1/x were related in a logarithmic fashion. Which would later pave the way for the anti-derivative of 1/x (Coolidge, 1950, p. 592) -
The number e is found to be related to compound interest by Jacob Bernoulli.
In the early to mid 1600's international trade was growing very quickly. This led to exploration into compound interest. The equation S=P(1+r/n)^(nt) could be used to find interest where P=principal, r=interest rate, t=years, and n=the number of compounds per year. Bernoulli noticed that if rate, principal, and years are set to 1 then the value S converges somewhere between 2 and 3.Thus Bernoulli first expressed e in limit notation without noticing it as a special number (Maor, 1994, p. 118) -
The number e is used in the solution of the catenary problem.
After the invention of calculus the Bernoulli brothers proposed the problem of finding the equation of the curve of a hanging chain or catenary in Leibniz's journal. Three mathematicians were able to solve it correctly Huygens, Leibniz, and Johann Bernoulli. The solution they found came out to be y=(e^(ax)+e^(-ax))/2a in today's terms. The number e however did not have a special symbol yet and the exponential equation was only thought of as the inverse of a log (Maor, 1994, p. 140-142). -
Leonhard Euler publishes "Introduction to Analysis of the Infinite", which is the first use of notation e.
The first notation of the number e that we use today was made by Euler in his "Introduction to Analysis of the Infinite." Euler gave independent definitions of the natural log and exponential equations that were based on limits whereas before, the exponential equation was only thought of as the inverse of the logarithm function. Using his definition of the exponential equation Euler was able to create a power series that estimated e correct to 18 decimal spaces (Maor, 1994, p. 155-157) -
Hermite proves the transcendence of the number e.
