Ultra wide angle lens the difference is only whether distortion is present or not. However, the shorter the focal length, the more difficult it is to implement rectilinear correction. In fisheye lenses, the visual angle is close to or more than 180 degrees in at least one direction. For example, a "diagonal fish eye" would have a viewing angle of at least 180 degrees within the diagonals of the frame. A "circular fisheye" would represent the image in the form of a circle. Rectilinear ultra-wide angle lenses are used in photography and cinematography sometimes to achieve three-dimensional perspective distortion instead of simply two-dimensional barrel
Revolutions in Mathematics Revolutions in Mathematics Revolutions in Mathematics is a collection of essays in the history and philosophy of mathematics. The book was reviewed by Pierre Kerszberg for "Mathematical Reviews" and by Michael S. Mahoney for "American Mathematical Monthly". Mahoney says "The title should have a question mark." He sets the context by referring to paradigm shifts that characterize scientific revolutions as described by Thomas Kuhn in his book "The Structure of Scientific Revolutions". According to Michael Crowe in chapter one, revolutions never occur in mathematics. Mahoney explains how mathematics grows upon itself and does not discard earlier gains in understanding with