Mathematics Department Colloquium
The History of Logarithms:
Friday, October 14, 2016
Most students learn about logarithms in intermediate algebra and elementary functions using exponential functions and the concept of an inverse function.
The early history of logarithms had some less obvious (from today's viewpoint) origins related to geometric and arithmetic rates of change and finding areas related to hyperbolas.
Professor Flashman will examine some of this early history of logarithms including
(I) Napier's 1616 original definition and tables of logarithms,
(II) the work of Gregoire de Saint-Vincent in 1647, and
1676 approach to estimating some values of natural (or hyperbolic) logarithms.
A table (based on 100) that demonstrates the idea.
How would one use Napier's Tables:Example: The rule of 3.Napier's logarithm tables.
Suppose a/b = c/d.
Given any three of these values, find the fourth.
Napier's Theorem: If a/b=c/d then
NOG(a)- NOG(b) = NOG(c)-NOG(d)
Making Napier logarithm tables. (MS Excel)
If time permits (at the end):
How do Napier logarithms compare with modern logarithms?