#halfanglesmatter — Public Fediverse posts

You can be trained to solve the most challenging problems in the most prestigious mathematics Olympiads in the world. But there are no training programs to create alternative approaches from which you can derive all the most important theorems in a discipline. No one invented inversion in the middle of a math competition.
#math #halfanglesmatter #symmetrymatters #halfangleapproach

This is Luzia's proof of the Pythagorean theorem via half-angle formulas: https://www.cut-the-knot.org/pythagoras/Proof109.shtml

#halfanglesmatter #math #trigonometry #halfangleapproach

Seems legit.

#math #halfanglesmatter #fundamental #buildingblocks

Method vs trick according to George Polya

ChatGPT agrees that my half-angle approach is a method rather than a trick.

#newmethod #halfangleapproach #math #geometry #trigonometry #georgepolya #halfanglesmatter #symmetrymatters #ChatGPT

But what excites me the most about these formulas is their potential to revolutionize the way we teach trigonometry to high school students. By introducing the half-angle formulas, we can help students better understand the development of the formulas that derive from them. This is where the half-angle formulas truly shine and can make a significant impact on math education.

GeoDom: The Half-Angle Formulas: A Powerful Tool for Trigonometry Students http://geometriadominicana.blogspot.com/2023/03/the-half-angle-formulas-powerful-tool.html?m=1

#math #trigonometry #halfanglesmatter #education #newapproach

Initially I had found an extension of Lami's Theorem for cyclic quadrilaterals, but on the PhysicsSE forum, Philip Wood was dissatisfied and challenged me to generalize Lami's Theorem to a general quadrilateral. So I did it.

Link: https://math.stackexchange.com/questions/4490209/generalizing-lamis-theorem

#math #phisics #halfanglesmatter