
MHB Master
#1
November 22nd, 2018,
07:46
I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard.
I am currently focused on Chapter 6: Forms and Vector Calculus ...
I need some help in order to understand some notes by H&H following Figure 6.1.6 ... ...
Figure 6.1.6 and the notes following it read as follows:
My question regarding the notes following Figure 6.1.1 is as follows:
What is the meaning/significance of the terms $ \displaystyle \text{ vol}_2$ preceding $ \displaystyle P_1, P_2$ and $ \displaystyle P_3$ ... indeed I can see no need for the terms at all ...
Can someone please clarify this issue ...
Peter
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It may help MHB readers of the above post to have access to H&H's section on the Geometric Meaning of kforms ... so I am providing the text of the same ... as follows:
Hope that helps ...
Peter

November 22nd, 2018 07:46
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#2
November 24th, 2018,
05:59
Hi Peter
I do not think that the notation is superfluous, but a better notation would be $vol_2(P_3)$, etc.
You have a parallelogram $P$ spanned by $\vec{v_1}$ and $\vec{v_2}$ in three dimensional real space.
$P_3$ is the projection of $P$ on the $(x,y)$plane.
$vol_2()$ is the action to compute the area of a plane, that is,
$vol_2(P_3)$ is the area of $P_3$

MHB Master
#3
November 25th, 2018,
04:09
Thread Author
Originally Posted by
steenis
Hi Peter
I do not think that the notation is superfluous, but a better notation would be $vol_2(P_3)$, etc.
You have a parallelogram $P$ spanned by $\vec{v_1}$ and $\vec{v_2}$ in three dimensional real space.
$P_3$ is the projection of $P$ on the $(x,y)$plane.
$vol_2()$ is the action to compute the area of a plane, that is,
$vol_2(P_3)$ is the area of $P_3$
Thanks for the insight and help, Hugo ...
Appreciate your help ...
Peter