There are many differences but perhaps the main difference is to do with the parallel postulate - or equivalently - the sum of the interior angles of a triangle. The sum of the interior angles of a triangle that is drawn on a spherical surface can be much greater than 180 degrees. One consequence is that given any line and a point that is not on that line it is possible to draw more than one lines through the point which will not meet the line.
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.
plane trigonometry spherical trigonometry
11/35
it helps human to servie
The two branches of trigonometry are plane trigonometry, which deals with figures lying wholly in a single plane, and spherical trigonometry, which deals with triangles that are sections of the surface of a sphere.
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.
plane trigonometry spherical trigonometry
Plane trigonometry is trigonometry carried out in (on) a plane. This could be contrasted with spherical trigonometry, which is trigonometry carried out on the surface of a sphere. Certainly there are some other more complex forms of trig.
11/35
it helps human to servie
The two branches of trigonometry are plane trigonometry, which deals with figures lying wholly in a single plane, and spherical trigonometry, which deals with triangles that are sections of the surface of a sphere.
spherical and plane trigonometry? :p
Several great mathematicians have made contributions to trigonometry. Pitiscus wrote books on plane and spherical trigonometry, and Hipparchus produced a table of chords.
John Hymers has written: 'A treatise on plane and spherical trigonometry, and on trigonometrical tables and logarithms' 'The Elements of the Theory of Astronomy' 'A Treatise on the Integral Calculus: Containing the Integration of Explicit Functions of One ..' 'A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ..'
Spherical trigonometry is important because the Earth is a sphere, not a plane, so if you wanted to get the distance between one point on Earth and another, plane trigonometry wouldn't give you the right answer. Plane trigonometry can be used to find the height of something without having to climb it, such as a flagpole or skyscraper. Trigonometry, whether spherical or planar, is used in engineering to design buildings, cars, ships, and planes. It is used in physics to calculate the properties of electric and magnetic fields. It is used in navigation, and projectile motion. It is also used in the design of musical chords and instruments, as well as lenses and optics.
Navigation takes place on the surface of a sphere, and it involves angles and distances. Spherical trigonometry was developed from plane trigonometry so that navigators could find their away over the Earth's surface.
There are more than two but the two most common ones are plane trig and spherical trig.