Articles

The binomial theorem expands (a + b)^n with Pascal’s triangle and C(n, k). See the general term, why coefficients sum to 2^n, and the link to probability.

Learn how heat makes solids and liquids grow, how to use dL = alpha x L x dT, and why rails, bridges and pipes need expansion gaps.

Capacitance is charge stored per volt. Learn the farad, Q = CV, the energy formula, the parallel-plate formula, series and parallel rules, and safety.

Wave speed equals frequency times wavelength. Learn the rule, the period, the right speed for sound and light, and how to avoid unit slips.

Work is force times distance times the cosine of the angle. Learn why work can be zero or negative, and how it links to energy and power.

Coulomb’s law says F = k q1 q2 / r^2. Learn what each symbol means, why like charges repel, and how the inverse square shapes the electric force.

Square each component, add, and take the root. Learn vector magnitude in 2D, 3D and beyond, plus unit vectors, direction angles and point distance.

The dot product returns a number built on cosine, and the cross product returns a 3D vector built on sine. See how each works and when to use it.

A 50 g print costs about 1.41 in filament, power and a failure allowance. Learn the formula, a quick reference table and what the cash cost leaves out.

Pot odds tell you the equity you need to call a bet. Learn the formula, how to count outs, the rule of 2 and 4, and when implied odds matter.