Mechanical Expressions Beta Extended
 We have extended the free beta period for our novel symbolic mechanics program Mechanical Expressions for a further 6 months.
The
beta will now extend till the end of September. If you are a
registered beta user, you should have been emailed a new key.
If you did not get a new key, you should just sign up again here.
Don't forget to give us your feedback, we are working to incorporate as many user comments into the final product as we can.

How to... model a bead sliding on a cycloid curve in Mechanical Expressions

An inverted cycloid curve is the solution to the brachistochrone problem: providing the quickest path between two points for a ball rolling under gravity, or a bead sliding on a wire.
Here is how to model this in Mechanical Expressions.
First create the cycloid: a parametric curve with X = T+sin(T), Y = 1cos(T) and with T varying from 3.14 to 3.14.
Now position a point on this curve and use Constrain/Proportional to constrain it to lie at parametric location t.
Select the point and use Mechanics Input/Mass to specify its mass.
Now select the parameter t and use Mechanics Output/Resultant Acceleration to compute its acceleration.
Now create an app using File/Export/HTML5 Javascript App.
Specify
that the app should contain a simulation, give it a start button, and
set t to be draggable. The result should look like this.
If you add a second bead on a line and a third on a manipulable curve, you can observe that the bead on the cycloid beats both. 
Anja Greer Conference
 Learn how to make eBooks for the iPad with interactive mathematical diagrams at the Anja S. Greer Conference on Mathematics, Science and Technology.
Philip
Todd will lead a 5 day workshop at the conference which will teach you
how to use Apple's iBook Author software in conjunction with Geometry
Expressions to create an interactive mathematical iBook.
Philip will share techniques he developed for his "24 Whimsical Clocks" iBook and for the interactive Euclid's Elements.
The conference takes place at the Phillips Exeter Academy June 22June 27 2014


Problem of the Month 
Last month's problem came from Archimedes De lineis spiralibus, (in Greek Peri helikon).
This month's problem is from his Liber Assumptorum, whose Greek version is lost, and whose attribution is uncertain.
But the problem could come from a modern test.
C
lies on the circumference of a circle centered at A. CD cuts the circle
at B. BD is the same length as the radius of the circle. DA
extended meets the circle in E.
What is the relationship between angle ADB and angle CAE?
An app which lets you explore this problem is here.




