RE: The Mathematical Proof Thread
September 10, 2017 at 10:38 pm
(This post was last modified: September 10, 2017 at 10:46 pm by Kernel Sohcahtoa.)
Hello everyone. I was working on a proof yesterday and thought that it was cool enough to share here. Hence, the proposition and my direct proof of it is below.
With that said, in creating this thread, it was my intent for people to be able to post whatever beauty they encountered in mathematics for as long as possible. Thus, I apologize if my post violates community guidelines or causes any inconvenience to the staff and/or AF members.
Proposition: For every four real numbers a,b,c, and d, sqrt(a^2 + b^2)*sqrt(c^2 + d^2) ≥ ac + bd.
Note the proposition can be re-written in “if-then” form, which yields the following equivalent statement: “if a,b,c, and d are real numbers, then sqrt(a^2 + b^2)*sqrt(c^2 + d^2) ≥ ac + bd.
Proof.
Notes
With that said, in creating this thread, it was my intent for people to be able to post whatever beauty they encountered in mathematics for as long as possible. Thus, I apologize if my post violates community guidelines or causes any inconvenience to the staff and/or AF members.
Proposition: For every four real numbers a,b,c, and d, sqrt(a^2 + b^2)*sqrt(c^2 + d^2) ≥ ac + bd.
Note the proposition can be re-written in “if-then” form, which yields the following equivalent statement: “if a,b,c, and d are real numbers, then sqrt(a^2 + b^2)*sqrt(c^2 + d^2) ≥ ac + bd.
Proof.
Notes