Stereographic Projection III: Pole of a great circle

[@insunghan7120]

Thanks for the very detailed lecture! The stereographic projection series are very helpful. Are you going to cover EBSD later?

[@jorgejacintozaratesalvatie4552]

Very well my friend

[@prabhuprasad2669]

Sir ,for geometrical analysis why do u rotated primitive circle by 90 not by 30 or 60 degree ,what is the reason!??

[@rajeshprasadlectures]

M and N lying on a diameter DE are projections of two perpendicular directions OX and OY lying in a vertical plane. But in the construction OX and OY lie in a horizontal plane, the plane of the primitive. Thus to justify the construction it is necessary to rotate the primitive by 90 degrees to coincide with the vertical plane. As we rotate, OX and OY rotate from horizontal to vertical position but M and N remain at the same location justifying that N is the projection of a direction (OY) perpendicular to the direction OX whose projection is M.

[@prabhuprasad2669]

Thank u sir very much.sir could u plz make videos on pole figures and inverse pole figures,their significance and how these are related to stereographic projection

[@palaniappankarthik]

Sir, Why is the diameter of primitive circle has infinite radius?

[@rajeshprasadlectures]

Its property of stereographic projection that all planes project as circles. Horizontal plane projects as primitive circle of radius R. As the planes tilts away from the horizontal the radius of the corresponding great circle increases. It can be shown, I have not done it as yet in any of my videos, but may be I should, that the radius of the great circle is R/cos (phi) where phi is the angle of the inclined plane from the horizontal plane. This clearly shows that as the plane tilts more and more, phi increases, and so the radius of the great circle. In the limit of the plane becoming vertical, the projection becomes a straight line, the diameter of the primitive. But in the interest of the continuity, this diameter is also considered a circle of infinite radius. This is consistent with the radius calculated by the above formula with phi =90 degree.

[@palaniappankarthik]

@@rajeshprasadlectures Thanks Professor

[@palaniappankarthik]

Sir, the projection of horizantal plane is called primitive circle. But why the projection of vertical plane called radius of primitive circle? Are we talking about the same primitive circle?

[@rajeshprasadlectures]

Yes, it is the same primitive circle. Please review the introductory video on stereographic projection for more details: kzbin.info/www/bejne/q4OwfpmlbJmbick