display | more...

The hyperbolic spiral originated with Pierre Varignon in 1704. It was studied by Johann Bernoulli between 1710 and 1713 and was also studied by Cotes in 1722.

The hyperbolic name reflects the relation between radius and angle being the same as the x,y relation for the hyperbola.

When a hyperbolic spiral is rolling over a line, then the path of the pole forms a tractrix.

It is considered a kind of Archimedean spiral.

Polar Equation:
r = a/θ

```                              ;fi
tji
iji
;ji.
if:
jj:
jj
:L:
fi
.fj
;f
f;
.L.
.L.
.G
.G
f
f.
;t
G
t;
.G
jf
Gi
f
G                            .tiitiiiiiii,
G                          iji:         .tjt
G,                       jf:                tf
Gi                      f.    iit;,iiji       fi
iL                     G    tj,jfGGfj: jj      it
f:                   .f   t;jDf,  ,fff ,j      f
L                    f   G GD     .Gtf G       #
j;                   G   f;GD,   :ELjt G       #
L.                  ,f   jjjGEGGGfff .f        #
L:                  :fi   iiiiiti  if        #
f,                   :tj;.    :ttt:        f#
tf                      ,iiii,           ;f
fi                                    ij
if:                                 jt
ijt                             tf.
iti.                      ;jj
,itti:            ,tiit:
###         ##
```

Log in or register to write something here or to contact authors.