The Most Useful Curve in Mathematics [Logarithms]

Welch Labs
Feb 3, 2024
7 notes
7 Notes in this Video

Logarithm Curve Turns Multiplication into Addition

Logarithms Multiplication Addition CurveMapping
0:00

Mathematicians and navigators who need faster computation use logarithms, and the video introduces a curve that maps numeric operations from one axis to another.

Napier’s Logarithm Tables for Navigation

LogarithmTables Navigation JohnNapier Computation
1:10

John Napier and early modern navigators needed faster ways to compute trigonometric ratios, and the video shows how logarithm tables transformed practical navigation.

Logarithms Count Exponents

Logarithms Exponents Powers Bases
4:40

Mathematicians analyzing powers and ratios use logarithms to track how many multiplications of a base produce a given number.

Napier’s Geometric Construction of Logs

LogarithmConstruction GeometricSequence JohnNapier Ratio
5:40

John Napier defined logarithms through a geometric process, and the video explains his construction using two moving points with linked motions.

Briggs Rebuilds Logs in Base 10

HenryBriggs BaseTen Logarithms Tables
7:10

Henry Briggs recognized that Napier’s base was awkward for practical work and proposed rebuilding logarithms using the decimal system that navigators and merchants already used.

Briggs Linear Approximation Near One

LinearApproximation Logarithms SquareRoots Precision
9:20

Henry Briggs needed high-precision base ten logarithms, and the video shows how he used repeated square roots to reach a region where the log curve behaves nearly linearly.

Slide Rules Use Logarithmic Spacing

SlideRule LogarithmicScale Computation Multiplication
12:40

Engineers and navigators used slide rules for centuries, relying on the logarithmic spacing of tick marks to perform fast calculations without writing down long arithmetic.