// minds behind maths

Hipparchus of Nicaea

c. 190 – c. 120 BC · Astronomy, trigonometry

Hipparchus was a Greek astronomer and mathematician often called the father of trigonometry. To support his astronomical work he compiled the first known trigonometric table — a table of chords — which related the angles at the centre of a circle to the lengths of the chords they cut, the ancient forerunner of the modern sine. This linking of angles to side lengths is the foundation on which the sine, cosine, and tangent ratios were later built.

Source: Wikipedia — Hipparchus

Formulas that trace back to Hipparchus of Nicaea

Distance to a star by parallax distance (pc) = 1 / parallax (arcsec)

Impact angle of a trajectory impact angle = tan⁻¹(vertical drop / horizontal travel)

Measuring a tree's height height = distance × tan θ + eye height

Ocean depth from angled sonar depth = slant range × sin θ

Roof pitch and rafter length pitch = tan⁻¹(rise / run), rafter = √(rise² + run²)

Tracking an aircraft's altitude altitude = ground distance × tan θ