Immersive Geometry with Bogacki in Second Life

VLP Display is a Second Life object designed to display points, vectors, line segments, lines, and planes in 3D space. It was created by Prof. Przemyslaw Bogacki (2009) (aka Reaso Ning in SL) in an attempt to explore the potential of the Second Life platform in a collegiate mathematics learning and teaching. I've mentioned another work on normal vectors from Prof. Bogacki in a previous post.

It listens to commands on channel 33 from its owner.

Example 1 - Three vectors

  Let i be a vector in x direction.
  Let j be a vector in y direction.
  Let k be a vector in z direction.



The commands for this example were:
  /33 d "Example 1"

  /33 d "Let i be a vector in x direction."

  /33 i=v 10 0 0 blue "i"

  /33 d "Let j be a vector in y direction."

  /33 j=v 0 10 0 blue "j"

  /33 d "Let k be a vector in z direction."

  /33 k=v 0 0 10 blue "k"

Example 2 - A plane defined by two vectors

  Let v1 be a vector.
  Let v2 be another vector.
  p1 is the plane defined by v1 & v2



The commands for this example were:
  /33 d "Example 2"

  /33 d "Let v1 be a vector."

  /33 v1=v -1 4 6 "v1" blue

  /33 d "Let v2 be another vector."

  /33 v2=v -2 5 7 "v2" red

  /33 d "p1 is the plane defined by v1 & v2"

  /33 p1=pl 2 5 -3 3 "p1" yellow

Example 3 - Two planes intersecting in a line

  Let p1 be the plane 2x + y + 3z = 7.
  Let p2 be the plane x – y + z = 5.
  p1 & p2 intersect in the line l1 x=4t, y=t-2, z=-3t+3



The commands for this example were:
  /33 d "Example 3"

  /33 d "Let p1 be the plane 2x + y + 3z = 7."

  /33 p1=pl 2 1 3 7 "p1" blue

  /33 d "Let p2 be the plane x – y + z = 5."

  /33 p2=pl 1 -1 1 5 "p2" green

  /33 d "p1 & p2 intersect in the line l1 x=4t, y=t-2, z=-3t+3"

  /33 l1=l 4 0 1 -2 -3 3 "l1" red

VLP Display can understand many commands.

A notecard with a complete reference can be accessed by saying "/33 help" after the VLP Display is rezzed in SL.

A free copy of VLP Display can be obtained from the SL Marketplace:
https://marketplace.secondlife.com/p/VLP-Display/231164

References

Bogacki, P. (2009). Multivariable Calculus Virtual Office Hours in a Metaverse. In J. Foster (Ed.), CD-ROM Proceedings of the Twentieth Annual International Conference on Technology in Collegiate Mathematics, San Antonio, Texas, March 6-9, 2008 (p. C015). Upper Saddle River, NJ: Pearson Education. Retrieved from http://archives.math.utk.edu/ICTCM/i/20/C015.html