Projective Plane and Homogeneous Coordinates - FLT Proof #4.1.2.5

Описание: At last the climax of this little series on the projective plane! With a firm grasp of the basics of vector operations, we're ready to look at the projective plane and homogeneous coordinates. We are continuing to build a basic foundation with our survey of the topics we must explore far more deeply in order to understand the Proof of Fermat's Last Theorem.

We are almost done with this preliminary survey of some basics. From here on out, things are going to get more specialized and difficult. Please subscribe; it will be important to keep together as we move along. I'll want your help, and you won't want to miss anything!

The videos in this series are:

Part 1: Explanation and justification of the dot product.
Part 2: Explanation and justification of the determinant, and its relationship to the dot product.
Part 3: Cross Product #1. Explanation of and justification for what the cross product actually is, something you will find nowhere else on the internet.
Part 4: Cross Product #2. Proof that the cross product returns a vector perpendicular to the plane containing the two vectors. Something you will find nowhere else on the internet.
Part 5: Cross Product #3. Proof that the cross product returns a vector with magnitude equal to the area of the parallelogram inscribed by the two vectors.
Part 6: Equation of a Plane. Brief explanation of the equation of a plane and the vector normal to a plane.
Part 7: Projective Plane and Homogeneous Coordinates.

Please leave any questions, comments, or suggestions in the comments below!

The next videos after these will be:
#4.3 Elliptic Curves over Complex Numbers
#5. Then a very basic overview of Modular Forms, so he have a basic comprehension of what they are as well.
#6. With a basic understanding of Elliptic Curves and Modular Forms, I will give you a brief history of the proof, then my basic understanding of Wiles' proof--how does Taniyama-Shimura (every Elliptic Curve is a Modular Form) imply Fermat's Last Theorem. (This will be the culmination of these first five videos. I think this video will already do a better job of explaining Wiles' proof in basic terms than any currently on youtube.)

Please subscribe and support these videos on patreon:   / greg55666  

(Please join me on patreon. It only costs a dollar, and we have a long way to go to a complete understanding of the proof of Fermat's Last Theorem!)

The math in this video was learned in part from two videos by Norman Wildberger.    • Projective geometry and homogeneous coordi...   and    • Lines and planes in projective geometry | ...