Livio’s Mathematical Creations with Phun
Are you having Phun Yet?
In my last Post I mentioned the incredible physics sand box or physics reality simulator Phun . Here I will explain in some detail one scene created with Phun.
When you build physical simulations in Phun you are creating a visual representation that is attached virtually near physical behavior. In a way you are actually building graphically a very sophisticated computer program where each element have physical properties. Like being able to move, collide, bounce, gravity, velocity, acceleration etc. Naturally the simulation is no perfect but is very close to reality and that is what makes it very surprising and I believe useful. It’s almost like using Lego blocks but this time you can build the building blocks by yourself!
I will name the process of building scenes “Phun programming” for the above reason and by extension a Phun programmer is he who creates a scene.
While many of the Phun programmers restrict them self to creating rockets and tanks some others have dedicated their time to create ingeniously intricate mechanism. I am still in complete awe by some of the mechanical things that people have created with Phun. Between those prolific creators I have found Livio Zucca from Turin Italy the home of world fame mathematician Giuseppe Peano. I believe Livio’s creations deserve more attention for his ingenuity.
In my prior post about the Pascal triangle with Phun I extended a prior idea from Livio. The machine in question is a binary mechanical counter.
The main component to perform computations in this particular device is what is know as a latch and it should not be confused with a flip-flop. The main difference between latch and flip-flop is that latches are transparent storage elements while flip-flops are not. Wikipedia point out this new distinction.
In the above picture you can see a magnified section of the machine. This we called the ball feeding mechanism and it’s function is to collect balls and feed them up the two dimensional vertical tube on the left.
Let us explained in a bit of detail how this is achieve with Phun.
In Phun you can simulate gravity and can also simulate movement. You can define two types of hinges. The normal kind that is just a hinge that hinges and there is the one that can act as an engine or motor. This is just a programmatic simplification on Phun’s designer part. It will be nice if there was some visual differentiation between them but at the moment there is none.
The crosses are used to attached things so they will not fall off the scene when gravity acts upon them.
Notice the green bar at the bottom of the picture. That bar acts as the collector of balls and it does have a very slight inclination this is useful in this design as it makes the balls roll slowly towards the left where the feeding mechanism is located.
You can also see a spring and I guess you must probably already know what a spring does!
and at last the actual latch
The latch acts like a balance and there is a hinge that can be visible if you magnify the picture a little bit more. The numbers have a double function in this particular case. They act as stoppers for the balancer and also as indicators of the state of the latch. As portrait above this latch is in 0 state.
As you probably know latches have two states. One can be use to represent 0 state as in this case and the other can be use to represent 1.
The latch alternates between this two states as you can see in the animation below.
You may also appreciate the mechanism for translating circular motion into linear upward motion on the left side. This mechanism brings back memories of the mechanism that provided steam locomotive with motive power in time past.
As you may have already guess by the picture of the machine and the name the function of this particular mechanism is to count balls dropping down from the device and this is done using the binary numerical system. The binary system is a numerical positional system that uses only two digits instead of the 10 digits we use in our decimal numerical system.
For educators Phun will be a source of inspiration. I believe it is very useful for the instruction and motivation of Mathematics,Physics, Computer Science, Mechanical Engineering,Electronics. Phun is opening a new universe of interactive learning and should I dare also say FUN!
If you like to play,run or modify the Scene above in the Phun simulator you can download the Phun program and the scene from
If you like to see a short video of my modification then go
I am planning to make more Posts with the Best of Livio’s Phun Machines.
We will also post a video lecture about Phun at www.isallaboutmath.com
