The term "reciprocal proportion triangle" is used in this work to describe a triangle whose side lengths are in the proportion
.
In order for such a triangle to exist, Tte triangle
inequality requires
 |
(1)
|
When combined with the requirement that side lengths be positive, the values of 
for which a reciprocal proportion triangle exists are 
, i.e., 
, where 
is the golden ratio.
This means that reciprocal proportion triangles do not exist for common constants like 
,
,
the golden ratio 
, and the Khinchin constant 
.
However, they do exist for the Kinkelin-Glaisher
constant 
, plastic constant 
,
supergolden ratio 
, and square root of the golden
ratio 
.
The following table summarizes some reciprocal proportion triangles.
 | triangle |
supergolden ratio  | supergolden triangle |
square root of golden
ratio  | Kepler triangle |
plastic
constant  | plastic triangle |
When a reciprocal proportion triangle exists with ratio 
, it has area
 |
(2)
|
and angles
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
Pegg (2016) terms such triangles "power triangles."
