In my last post Curvature, I showed how the curvature, along a path is equal to: . I then asked a “challenge” question about how one could compute the curvature without referencing a velocity or acceleration vector. I have slightly rephrased the question below: Is…
Blog Archives
Curvature
There is a natural way to compute the curvature for a curve whose position is given as a function of time, . The following is the vector proof which shows how the velocity and acceleration vectors can be used to compute the curvature at any time. Is there…
Tagged with: curvature, Multivariable calculus, open question, vector proof
Posted in Multivariable Calculus
Posted in Multivariable Calculus
Christmas Fractal Competition Vote!
Your SAS Multivariable Calculus Class presents… The Second Annual Christmas Tree Competition! Vote for your favorite here!
Posted in Multivariable Calculus
An end and a new beginning…
Check out the prezi for a summary of our 2 week experiment You’ll find out what our students thought of the experiment. I hope you enjoyed it as much as we did and find their reflections helpful!
Posted in Advanced Chemistry, Multivariable Calculus
The power of aggregation – part 2
In part 1, I argued that many of the most compelling processes that we observe in the world around us work according to a basic principle associated with aggregation. I will expand on this by writing a few lines that…
Posted in Advanced Chemistry, Multivariable Calculus
The power of aggregation – part 1
This is the information age, and sitting at the heart of the information expansion that has defined this age is a simple idea: aggregation. Swimming in all this information, will humans ever be able to reliably predict the future? And…
Posted in Advanced Chemistry, Multivariable Calculus
Engineering scientific discovery
I was recently listening to archived Radiolab episodes, and came across this story about Eureqa, a computer algorithm that looks for patterns in data sets. The amazing thing about this story is that the algorithm finds correlations and relationships between…
Tagged with: Algorithm, Artificial intelligence, Data set, eureqa, Google, Machine learning, Newton, Newton's laws of motion, Radiolab
Posted in Advanced Chemistry, Multivariable Calculus, Steven Strogatz
Posted in Advanced Chemistry, Multivariable Calculus, Steven Strogatz
The Magic of Balance Pt. 2 (Center of Mass)
Continued from my last post, I further researched into the calculation for center of mass. Today’s post is going to be about how we derive the equations for center of mass. Mass First we need to define the mass of an…
Tagged with: Balance, Center of mass, Moment, Probability density function, Proof
Posted in Multivariable Calculus
Posted in Multivariable Calculus
Epic infinite imbalance problem!
I really can’t get enough of these puzzles. Thanks to Paul Salomon for describing them. Go check out his work over at Lost In Recursion if you haven’t seen it yet. I would love to see what kinds of puzzles…
Tagged with: imbalance problems, infinite imbalance problems
Posted in Advanced Chemistry, Multivariable Calculus
Posted in Advanced Chemistry, Multivariable Calculus
The number of photons ejected from the sun in a second
How many photons does the sun emit in a second? The following worksheet was used in companion with this post for chemistry students. Our chemistry class used the work of Brian Cox and (originally) John Herschel to determine the number…
Tagged with: Advanced Chemistry, Multivariable calculus
Posted in Advanced Chemistry, Multivariable Calculus
Posted in Advanced Chemistry, Multivariable Calculus
harveyjohnson
scenic-science + thematic-mathematics | same 