Operations on Bivectors - From Zero to Geo 2.2

What can we do with bivectors? While we won't get to the best of bivectors until chapter 3, in this video we explore the basic operations we can do on bivectors. We start with looking at the magnitude of a bivector and how to scale them, and then we move onto addition, both in two dimensions and three dimensions.

Patreon Supporters:
David Johnston
Jason Killian
jerrud
Richard Penner
trb

Sections:
00:00 Introduction
00:25 Magnitude/Scaling
01:54 Magnitude/Scaling Exercise
04:04 2D Addition
05:15 2D Addition Exercise
06:24 3D Addition Qualitative
07:35 3D Addition Quantitative
08:36 3D Addition With Weird Shapes
09:30 3D Addition Pitfalls
10:46 Conclusion

[MeshremMath]

😃 I am quite excited that a new “From Zero to Geo” came out.

[kaiko]

This is the best resource for geometric algebra so far! Can't wait to get to the more bloody mathematical details of the algebra 😂

[nullmeasure]

Thank you so much for working so hard! These are so useful for helping my friends who are still in school. You're much better at explaining things than I am.

[PUP-vc]

Thank you! This is something I will go back too!

[elementare.]

I was waiting for your videos too long. I hope you post videos from this series more frequently. It's with sure my favorite series on youtube

[SlackwareNVM]

It's been so long I was surprised to see the video. Great explanations!

[Whkk]

Can’t wait for the weirdness of 3D bivector subtraction.

[igorvaiman]

Amazing video as always, excited to continue following the series!

[johnwilson]

I'm pretty sure that I've lived my whole life pretending successfully that bivectors were just vectors that pointed normal to the plane of the bivector. D:

[isavenewspapers]

I have fun doing the exercises, even if it's all about stuff I already know for now. It's just nice to put pencil to paper and do some math.

[anselmschueler]

Some feedback: I think it would be more illustrative to show changing the sign of a bivector by visually flipping the vector as if rotated in 3D, rather than rotating the arrows.
More feedback: I think it’s important to highlight that for bivector subtraction, we want to end up with just one of the bivectors remaining, which only happens when one is fully contained in the other (or you could do it in multiple steps).

[linuxp]

The sum of bivector's dual/normal vectors have same effect, in 3D.

Take the areas (magnitudes) and plot each vector with the same magnitude, but in length, perpendicular to each bivector's plane. Remind, the sign of the normal vector is conventioned by right hand rule, i.e. the normal vector always rises up from the side where perimetral circulation seems anti-clockwise when looked from above.

Perform the additions/subtractions of all the normal vectors.

After that, plot a square or retangle with an area with the same magnitude of the resulting normal vector.

[goldeuberto]

the people who thought all of this, worked it visually in their minds, or by purely algebraic means?

[nakkikala]

Amazing, that I just got the full intuition of bivector addition before watching this. In crystallography, summing of the miller indices makes perfect geometric sense with bivectors. I just found it by myself (probably that is in some books/papers) and confirmed it geometrically by drawing on paper. Also reciprocal space is bivector space? The basis of it is defined with a cross product... But is this dual transform between real and reciprocal space a clifford fourier transform? Wavevector is a bivector? It would make sense to use a plane as a wavefront? Also wave vector of light, electromagnetic wave, could be a bivector? Don't know if that would better perspective in the case of light momentum, though. In case of crystallographic diffracton, the lattice planes are naturally bivectors, and the plane of crystal wave is naturally the bivectors of crystal vectors?

[davidhand]

When you're done with the basics, can you please go on to explain CGA (conformal geometric algebra)? There's very, very little info on CGA on YouTube.

[aza-joru]

Thank you for your great job, just a little question what about equality of bivectors in 3D, we all know that for usual vectors, they must have the same orientation, magnitude and direction (i.e. parallel lines) to be equal, in the case of bivectors what will we say? another question the form of bivectors can be a 3D form like a hemisphere?

[huseyinemreeken]

Bro I thought you were dead. Where have you been?

[be-mrtj]

Surely the orientation of bivectors can't exist in 3D, as simply rotating your viewoint will change the orientation. Am I missing something?