Journey of understaning logarithms

2024-06-25T16:56:41+00:00

Finally, I got a grip on logarithms. Why they came into being. First, I watched this video, from James Tanton - Logarithms: Brief History and Brief Mat.

• How logarithms relate to power
• Multiplying 3.156 * 3.456 * 2.876 by hand is very tedious

How they Invented Logarithms

• Introduces Jost who also contributed to logarithms

This book should have changed mathematics forever

• Jost Burgi’s Book

Series

From Logarithms: The Early History of a Familiar Function - Before Logarithms: The Computational Demands of the Late Sixteenth Century

• One method originating in the late sixteenth century that was used extensively to save computation was the technique called prosthaphaeresis, a compound constructed from the Greek terms prosthesis (addition) and aphaeresis (subtraction). This relation transformed long multiplications and divisions into additions and subtractions via trigonometric identities.
• their application specifically for multiplication first appeared in print in 1588 in a work by Nicolai Reymers Ursus

From History Victor Katz observed that Napier developed logarithms “for use in the extensive plane and spherical trigonometrical calculations necessary for astronomy

From https://locomat.loria.fr/napier/napier1619construction.pdf

• Mirifici logarithmorum canonis constructio
• Napier introduced a new notion of numbers and called them artificial numbers
• Napier took as origin the value 10^7(10 million) and defined its logarithm to be 0. Any smaller value x was given a logarithm corresponding to the ratio between 107 and x.

From Logarithms: The Early History of a Familiar Function - John Napier Introduces Logarithms

• Napier first published his work on logarithms in 1614 under the title Mirifici logarithmorum canonis descriptio, which translates literally as A Description of the Wonderful Table of Logarithms.
• Napier grounded his conception of the logarithm in a kinematic framework.
• To complete the tables, Napier computed almost ten million entries from which he selected the appropriate values. Napier himself reckoned that computing this many entries had taken him twenty years, which would put the beginning of his endeavors as far back as 1594.
• The motivation behind this approach is still not well understood by historians of mathematics

https://www.youtube.com/watch?v=habHK6wLkic&t=73s story of natural logarithms

https://www.youtube.com/watch?v=uMfnJ6TJinc

• where sin, cos came from
• SOHCAHTOA