Constants

Ratio of circumference to diameter of any circle. Irrational and transcendental.

Base of the natural logarithm. Defined as lim(n→∞) (1 + 1/n)ⁿ. Irrational and transcendental.

The positive root of x² = x + 1. Appears in geometry, sequences, and continued fractions.

Diagonal of a unit square. First known irrational number.

Height of an equilateral triangle with side 2. Appears in 30-60-90 triangles and hexagonal geometry.

Appears in the golden ratio and Fibonacci geometry.

Natural logarithm of 2. Useful in integration and series approximations.

Conversion factor between natural and common logarithms: log₁₀x = ln x / ln 10.

Used in number of digits problems: number of digits of n = ⌊log₁₀ n⌋ + 1.

Together with log 2, generates log values for 4, 6, 8, 9, 12 without a calculator.

Essential for combinatorics, binary, and inequalities.

Required for permutations, combinations, and series expansions.

22/7 overestimates π by about 0.04%. Use 3.14159 when precision matters.

25 primes below 100. Useful in number theory, GCD/LCM, and modular arithmetic problems.

1² through 20².

1³ through 10³.

Converges rapidly — 10 terms give e to 7 decimal places.

Converges very slowly — shown for conceptual value, not computation.

Appears in asymptotic analysis of harmonic series. Rarely tested directly but good to know.

The most-used inequality in JEE optimisation problems.

Equality holds when aᵢ/bᵢ is constant for all i.