I’ve written quite a few posts on mental math over the years. I think mental math is important/interesting for a couple reasons. First, there is some utility in being able to carry out small calculations with rough accuracy without having stop and open up a calculator. Second, the constraints imposed by mental calculation make you look at a problem differently, often in interesting ways. An approximate mental calculation often requires more understanding that a precise machine calculation.

Divisibility and factoring

• Divisibility by 2, 3, 4, …, 13
• Divisibility by base minus 1
• Divisibility by base plus 1
• John Conway’s factoring tricks
• Divisibility by any prime
• Fermat’s factoring trick

Day of the week

• Day of the week
• Year share

Transcendental functions

This page outlines how to calculate logarithms base 2, e, and 10, and their inverses, linking to other posts for details.

It also outlines computing trig functions, roots, and the gamma function. See the links below for more accurate ways to compute logarithms.

Incidentally, when I’ve posted about these approximations before, inevitably someone will say these are just Taylor approximations. No, they aren’t.

Logarithms

• Bidder’s logarithms
• Dorfler’s logarithms

Miscellaneous

• Radix conversion
• Squares
• Approximate factorials
• Mentally multiply by π
• Numbers worth remembering

The post Mental math posts first appeared on John D. Cook.