We took the word ‘vector’ and we made it a verb.
We created a realm where vectors would always be Geometric Vectors.
We then did a rework on everything from Counting to Linear Algebra. We did this with the intent that when a student gets to tensors, those strange things learned will make more sense.
There are several times a student in Tensor Calculus asks “How did you know to do that?” We are respectful of the answers we’ve seen teachers give and we want to try a different answer.
“We didn’t.”
We collected data and after we looked at the patterns, we went to the Math Store and asked the owner “Do you have anything that does this?”
We walked out of the store with two packages in our shopping bag, Linear Algebra and Tensor Calculus.
When we get to Linear Algebra, we will point back to homework problems you did with Addition and Multiplication and the Distributivity studied in Algebra. We will build coordinate systems out of nickels, dimes and quarters and then we will talk about the Invariance of a dollar.
Vector everything.
Dot Product of Four Vectors
We are going to use the metric signature (-,+,+,+). The dot product of two four-vectors, and , can be expressed as: Here, represent the components of vector and represent the components of vector . Discussions on this topic will probably mention a Minkowski metric. We used… There is a matrix that corresponds to the Minkowski…
Two Moments in Time
Our hypothesis here is that sometimes when you do a physics calculation and you get two answers and you recognize one as being sensible… …there might be something interesting about the “nonsense” answer. A student does a calculation and gets a positive answer and a negative answer and says “we can’t go back in time,…
Initial Conditions and Related Things
You are a secret agent. You have ten seconds to use your secret cell phone to tell everyone where you are located. Assume you know the vehicle has been traveling for two hours at 60 miles per hour eastward on a straight road that goes in the east direction. With what you know right now…
Vectoreverything 