Models
In the Poincaré disk model of the hyperbolic plane, an ideal triangle is bounded by three circles which intersect the boundary circle at right angles. In the Poincaré half-plane model, an ideal triangle is modeled by an arbelos, the figure between three mutually tangent semicircles. And in the Beltrami–Klein model of the hyperbolic plane, an ideal triangle is modeled by a Euclidean triangle that is circumscribed by the boundary circle. Note that in the Beltrami-Klein model, the angles at the vertices of an ideal triangle are not zero, because the Beltrami-Klein model, unlike the Poincaré disk and half-plane models, is not conformal i.e. it does not preserve angles.
Read more about this topic: Ideal Triangle
Famous quotes containing the word models:
“Friends broaden our horizons. They serve as new models with whom we can identify. They allow us to be ourselves—and accept us that way. They enhance our self-esteem because they think we’re okay, because we matter to them. And because they matter to us—for various reasons, at various levels of intensity—they enrich the quality of our emotional life.”
—Judith Viorst (20th century)
“Grandparents can be role models about areas that may not be significant to young children directly but that can teach them about patience and courage when we are ill, or handicapped by problems of aging. Our attitudes toward retirement, marriage, recreation, even our feelings about death and dying may make much more of an impression than we realize.”
—Eda Le Shan (20th century)
“The parents who wish to lead a quiet life I would say: Tell your children that they are very naughty—much naughtier than most children; point to the young people of some acquaintances as models of perfection, and impress your own children with a deep sense of their own inferiority. You carry so many more guns than they do that they cannot fight you. This is called moral influence and it will enable you to bounce them as much as you please.”
—Samuel Butler (1835–1902)