Hyperbolic coordinates
Geometric mean and hyperbolic angle as coordinates in quadrant I / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Hyperbolic coordinates?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane
- :\ x>0,\ y>0\ \}=Q} .
Hyperbolic coordinates take values in the hyperbolic plane defined as:
- .
These coordinates in HP are useful for studying logarithmic comparisons of direct proportion in Q and measuring deviations from direct proportion.
For in take
and
- .
The parameter u is the hyperbolic angle to (x, y) and v is the geometric mean of x and y.
The inverse mapping is
- .
The function is a continuous mapping, but not an analytic function.