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This workshop starts with a thorough investigation of functions and their graphs (operations, symmetries, stretches, translations, and inverses). Specific functions studied include polynomial, exponential, and logarithmic functions. Real world applications of functions are an important focus of many discussions. Other topics such as sequences and series, conic sections, and limits are covered as time permits. Prerequisite: Algebra II.
Non-Euclidean Geometry Online: a Guide to Resources
Area of a circular surface grows differently in each type of geometry. In Euclidean planar geometry it grows proportional with the square of the radius of the circle. In hyperbolic geometry it grows exponentially with the growth of the radius. In spherical geometry the area grows with the radius but it cannot exceed the area of the whole spherical surface.
Academic resources for the study of hyperbolic geometry
Successful completion of the Volunteer Corps program provides Choate Rosemary Hall students with the community service hours required for graduation.
A combination of and hyperbolic geometry can be found at the .
It can be shown that in each type of non-Euclidean geometry the sum of the interior angles of a triangle is directly related to the area of the triangle. Also, the area of a geometrical figure depends on “how much curved” the surface is – on the curvature of the surface.
Paleolithic art: Cro-Magnon man
From Daina Taimina’s collection of crocheted hyperbolic planes, the following has a triangle marked in light colors; the measures of the angles add up to less than 180 degrees: