Precession
The direction of Earth’s axis changes slowly. Hipparchus recognised a shift in stellar positions by comparing observations from different times.
08 / ANTIQUITY TO THE RENAISSANCE
Hipparchus of Nicaea
Astronomers can measure the angle between two directions in the sky. A circle turns that angle into a length they can calculate with.
Explore the mathematics ↓
01 / CHORDS & ANGLES
Turn an angle into a length
Astronomers can measure the angle between two stars, but not the distance. To calculate with angles, Hipparchus turned them into lengths.
Put the angle at the centre of a circle. The straight line joining the two rim points is a chord. A table of chords turns any angle into a length.
How far apart are two stars?
You can only measure the angle between them. Swing the sighting arm onto a star, then record its chord in the table.
Angle between the stars
=Chord length
=Chord
From chords to modern trigonometry
Cut the angle and the chord in half. Each half-chord divided by the radius is what we now call the sine of half the angle.
So chord = 2 × radius × sin(angle ÷ 2). Hipparchus’s table did the same job before sines existed.
THE IDEAEach angle has exactly one chord, but twice the angle does not give twice the chord. A table of chords lets you swap angles for lengths: the job trigonometry still does.
The person behind the ideas
- Worked as an astronomer in the second century BCE.
- Used earlier observations, including Babylonian astronomical records.
- Is associated with an early chord table and the discovery of the precession of the equinoxes.
More of the mathematics
Astronomical prediction
He developed mathematical models and measurements for the motions of the Sun and Moon.