Search results
Results from the WOW.Com Content Network
On the Sphere and Cylinder (Greek: Περὶ σφαίρας καὶ κυλίνδρου) is a treatise that was published by Archimedes in two volumes c. 225 BCE. [1] It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder , and was the first to do so.
How the Earth is projected onto a cylinder. The projection: is cylindrical, that means it has a cylindrical projection surface [2] is normal, that means it has a normal aspect; is an equal-area projection, that means any two areas in the map have the same relative size compared to their size on the sphere.
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
Lambert's projection is the basis for the cylindrical equal-area projection family. Lambert chose the equator as the parallel of no distortion. [2] By multiplying the projection's height by some factor and dividing the width by the same factor, the regions of no distortion can be moved to any desired pair of parallels north and south of the ...
A surface which obeys Lambert's law is said to be Lambertian, and exhibits Lambertian reflectance. Such a surface has a constant radiance / luminance , regardless of the angle from which it is observed; a single human eye perceives such a surface as having a constant brightness, regardless of the angle from which the eye observes the surface.
Lines, L. (1965), Solid geometry: With Chapters on Space-lattices, Sphere-packs and Crystals, Dover. Reprint of 1935 edition. A problem on page 101 describes the shape formed by a sphere with a cylinder removed as a "napkin ring" and asks for a proof that the volume is the same as that of a sphere with diameter equal to the length of the hole.
A cross sectional view of the sphere and a plane tangent to it at S. Each point on the sphere (except the antipode) is projected to the plane along a circular arc centered at the point of tangency between the sphere and plane. To define the Lambert azimuthal projection, imagine a plane set tangent to the sphere at some point S on the
A proof of the recursion formula relating the volume of the n-ball and an (n − 2)-ball can be given using the proportionality formula above and integration in cylindrical coordinates. Fix a plane through the center of the ball. Let r denote the distance between a point in the plane and the center of the sphere, and let θ denote the