MHB Prove Centroid Goes Through It

Thread starter slwarrior64
Start date Nov 4, 2020
Tags

Centroid

AI Thread Summary

The discussion centers on the necessity of proving that a line or shape must pass through its centroid. Participants express understanding of the concept but struggle with the mathematical proof required to substantiate it. One user indicates they have resolved their initial confusion but seeks assistance with a separate, related question. The conversation highlights a common challenge in geometry regarding centroids and their properties. Clarifying the proof of centroid properties remains a key focus.

Nov 4, 2020

slwarrior64

I can see how it would go through the centroid, but I don't know how to prove that it HAS to go through the centroid.

Mathematics news on Phys.org

Nov 6, 2020

slwarrior64

slwarrior64 said:

I can see how it would go through the centroid, but I don't know how to prove that it HAS to go through the centroid.
View attachment 10812

I figured it out but please help me with the other question I posted!

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...

View full post »

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

View full post »