Deep dives, practical guides, and incident analyses from engineers who build Safeguard. No fluff, no vendor FUD — just what you need to ship secure software.
Line multiplication draws each digit as sticks and counts the crossings per zone. Worked on four problems, proved with algebra, and its name checked.
How the Trachtenberg system multiplies by 11, 12, 5 to 9 and any number, adds and divides, worked step by step on fixed problems, with its real history.
How world champion mental calculators actually work: left to right addition and multiplication, criss-cross, squaring near round numbers, cube roots and the Doomsday rule, worked step by step with measured records.
How Maya mathematics works: base 20 bar and dot numerals, the shell zero, the Long Count's 18 x 20 step and calendar arithmetic, with every step worked.
How Babylonian base 60 works, why reciprocal tables made division fast, how YBC 7289 got √2, and what Plimpton 322 may be, with worked examples.
How Chisanbop works: thumbs worth 5 and 50, fingers worth 1 and 10, complements for adding and subtracting, and our full problem set worked finger by finger.
How the lattice, Napier's bones and the slide rule turned multiplication into addition, worked step by step on seven problems, with their precision limits.
How Egyptian doubling and Russian peasant halving multiply, divide and build unit fractions, why both are binary, and how CPUs still use shift and add.
Sample faster than twice the highest frequency and a band limited signal can be rebuilt. Worked examples from CD audio, G.711 phones, aliasing and SDR.
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