Editing Hyperbolic spiral (section)

=== Central projection of a helix ===
[[File:Schraublinie-hyp-spirale.svg|thumb|upright=0.8|Hyperbolic spiral as central projection of a helix]]
The [[central projection]] of a helix onto a plane perpendicular to the axis of the helix describes the view that one would see of the guardrail of a [[spiral staircase]], looking up or down from a viewpoint on the axis of the staircase.{{r|hammer}} To model this projection mathematically, consider the central projection from point <math>(0,0,d)</math> onto the image {{nowrap|plane <math>z=0</math>.}} This will map a point <math>(x,y,z)</math> to  the {{nowrap|point <math>\tfrac{d}{d-z}(x,y)</math>.{{r|loria-roever}}}}

The image under this projection of the helix with parametric representation
<math display=block>(r\cos t, r\sin t, ct),\quad c\neq 0,</math>
is the curve
<math display=block>\frac{dr}{d-ct}(\cos t,\sin t)</math>
with the polar equation
<math display=block>\rho=\frac{dr}{d-ct},</math>
which describes a hyperbolic spiral.{{r|loria-roever}}