Archimedes’ spiral

Definition

Archimedes' spiral is a curve represented in polar coordinates by the equation $r = a + b\theta$. It describes a spiral that moves away from the origin at a constant rate as the angle increases.

5 Must Know Facts For Your Next Test

1. The general form of Archimedes' spiral is $r = a + b\theta$, where $a$ and $b$ are constants.
2. As $\theta$ increases, the distance from the origin increases linearly.
3. The spiral has applications in fields such as physics, engineering, and computer graphics.
4. It differs from logarithmic spirals where the distance from the origin grows exponentially with increasing angle.
5. Graphing Archimedes' spiral involves plotting points for various values of $\theta$ and connecting them smoothly.

Review Questions

• What is the general equation for Archimedes' spiral?
• How does an increase in $\theta$ affect the distance from the origin?
• In what fields might you find applications of Archimedes' spiral?

Related terms

Polar Coordinates: A coordinate system where each point on a plane is determined by an angle and a distance from a reference point.

$r = \theta$: Equation representing another type of spiral known as Euler's Spiral or Cornu Spiral.

$r = ae^{b\theta}$: Equation representing a logarithmic spiral, where the distance from the origin grows exponentially with increasing angle.