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GraphingCalcUsers · User group for Pacific Tech's Graphing Calculator math education visualization software

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  • Members: 478
  • Category: Education
  • Founded: Dec 12, 2000
  • Language: English
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Messages 1949 - 1978 of 1978   Oldest  |  < Older  |  Newer >  |  Newest
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1949 Chris Young
c56young Send Email
Feb 4, 2013
7:10 pm
Using colored dots has the advantage of being able to do projections and sections with the minimum modification of the formula. A better color scheme would...
1950 Chris Young
c56young Send Email
Feb 4, 2013
11:04 pm
This is at least a visual demonstration, if not an analytical proof, that of all shapes of rectangular solids, the cube is the one will maximize the volume for...
1951 Bo Johannesson
bo.johannesson Send Email
Feb 7, 2013
3:13 pm
How can I do to make a movable point to show up both in the density plot and the surface plot? Regards, Bo Johannesson...
1952 Chris Young
c56young Send Email
Feb 7, 2013
11:11 pm
... You just need to use "[x' y' z'] = " and your point coordinates, as shown below....
1953 Christopher Young
c56young Send Email
Mar 7, 2013
3:45 am
Work in progress towards using eigenvectors to align 2nd degree conic sections to the axes. Would like to find an approach which generalizes to aligning cubic...
1954 Bo Johannesson
bo.johannesson Send Email
Mar 14, 2013
11:04 am
Hej! I can’t restrict the domains plotted by specifying intervals for x and y in a Density Plot by entering something like this: ...
1955 Christopher Young
c56young Send Email
Mar 14, 2013
12:40 pm
... will do it. I'm not sure why GC demands the "if" clause here, and won't allow the other form of clipping. On Mar 14, 2013, at 5:11 AM, Bo Johannesson <...
1956 Christopher Young
c56young Send Email
Mar 16, 2013
11:47 am
Work in progress showing that a sort of generalized Pythagorean relationship comes out of linear algebra on Euclidean space. Just as the projections of a line...
1957 Bo Johannesson
bo.johannesson Send Email
Mar 16, 2013
5:46 pm
Hej! Would it be possible to use Subscript in Summation and directly get the numerical result as it is in an example with Dot Product? Is it OK to use i as a...
1958 Ron Avitzur
rxa31107 Send Email
Mar 16, 2013
6:00 pm
... Yes, though it can cause confusion in some contexts. Best regards, Ron Avitzur...
1959 Christopher Young
c56young Send Email
Mar 18, 2013
11:26 am
Ron, In the example below with the column vector times the row vector, isn't it inconsistent to require the dot for this, since it's really just a kind of...
1960 Christopher Young
c56young Send Email
Mar 18, 2013
1:18 pm
I'm still having the same problem with row and column vectors when the components are _not_ elements of a table. At least for the case when the variables are...
1961 Bo Johannesson
bo.johannesson Send Email
Mar 19, 2013
9:02 pm
Hej! Is my attached DotProduct.gcf a good way to show how to, in Graphing Calculator, apply the algebraic definition and illustrate the example from Wikipedia...
1962 Christopher Young
c56young Send Email
Mar 20, 2013
6:55 am
... As a workaround, putting the written-out vectors into new variables will work....
1963 Ron Avitzur
rxa31107 Send Email
Mar 20, 2013
3:40 pm
Another alternative, for the table data: Sum(ab) will do the same....
1964 Bo Johannesson
bo.johannesson Send Email
Mar 22, 2013
10:24 am
Hej! I have made a document which illustrates two vectors in the x,y-plane and the angle between them. The way I do to plot the arc between the vectors is...
1965 Christopher Young
c56young Send Email
Mar 22, 2013
12:51 pm
The determinant always equals . This can be seen from the diagram above, where the length of MB times the length of VA gives the area of the parallelogram on...
1966 Christopher Young
c56young Send Email
Mar 22, 2013
2:07 pm
The determinant formula and the inner product formula (in 2D Euclidean space) together form 2 functional equations which I think uniquely specify the sine and...
1967 Christopher Young
c56young Send Email
Mar 22, 2013
2:13 pm
Actually, maybe it's more intuitive to get our definitions of the inner and outer products (= determinant, in the 2D case) from the projection functions we use...
1968 Christopher Young
c56young Send Email
Mar 22, 2013
2:18 pm
... If you just want the small angle between vectors drawn from the origin, it's enough to use . But, even then, we've got to correct for the case when the...
1969 Christopher Young
c56young Send Email
Apr 3, 2013
2:38 pm
The idea is that we have to prevent each succeeding vector from projecting on any of the previously orthogonalized vectors. Then we're guaranteed to have an...
1970 Christopher Young
c56young Send Email
Apr 8, 2013
1:59 pm
Non-square matrices are either "embedding&quot; or "detaching&quot; mappings. This one, , takes the vector that follows and "embeds" it in the subspace of xyz-space...
1971 Christopher Young
c56young Send Email
Apr 8, 2013
2:04 pm
[OK, I got a little carried away by my frustration at the total lack of interest I'm getting from everyone on what I think are exciting discoveries. Not...
1972 Christopher Young
c56young Send Email
Apr 9, 2013
5:11 am
Below, I've used non-square matrices in two ways: once, via , to map the gray circle in the 2D view to the slanted plane in the 3D view, and secondly, via the...
1973 Christopher Young
c56young Send Email
Apr 9, 2013
5:15 am
[I forgot to include the expressions for the circles and dots in the previous posting.] Below, I've used non-square matrices in two ways: once, via , to map...
1974 Christopher Young
c56young Send Email
Apr 10, 2013
5:11 pm
If we use the matrix-product versions of projections onto a line and a plane, we save some computation. It's also visually clearer. We Just back off on each...
1975 Christopher Young
c56young Send Email
Apr 12, 2013
6:39 pm
Here, we streamline the orthogonalization by using the formula for projection onto the plane determined by unit vectors u and v: We use the matrix identity . ...
1976 Christopher Young
c56young Send Email
May 1, 2013
12:41 pm
This is based on the derivation at http://math.stackexchange.com/questions/117418/projection-to-the-plane-in-the-direction-of-the-vector...
1977 Christopher Young
c56young Send Email
May 1, 2013
12:47 pm
If we restrict the test point to the z = 0 plane, then we have the same coordinates for its projection in the projected grid, as we'd expect for a linear...
1978 Christopher Young
c56young Send Email
May 6, 2013
10:09 am
The projection of a cube onto the diagonal plane specified by x + y + z = 0 will yield a hexagon with each of the parallelograms taking up two segments. ...
Messages 1949 - 1978 of 1978   Oldest  |  < Older  |  Newer >  |  Newest
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