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In our last two blog posts at blog.isallaboutmath.com we wrote about a new incredible computer program
called Phun (now Algodoo) available at http://www.algodoo.com/ this computer program is defined by his creator
Emil Ernerfeldt from Sweden as a 2 D physics sand box. Phun is a virtual physics reality
simulator. Imagine a computer program where you can build objects and this objects have
mass and gravity affecting them or collision between objects can also happen. You could
build objects of different shapes and sizes and also with different physical properties.
You may also be able to change what object collides with what other object by keeping
them in the same collision group. Since phun (algoodo) is 2D been able to set groups of
collision is a necessary property You are also allow to change the way of an object
bounciness friction and color. Naturally this is a simplification of the physical attributes
an object can have but it is the necessary minimum to produce a more or less convincing
physical simulation. The brush could be use for creating arbitrary shaped objects. You
may also create circles and boxes, chain and springs. The fix is use to attach things to
the background or to each other and the hinch have a dual purpose. It can be used as just
a hinch or as a motor. Phun (Algoodo) can be use as a creating tool
for experimenting with some mechanisms or mechanical interactions. In a way Phun (Algoodoo)
is similar to Lego blocks but with phun you could create your own virtual parts. If you
visit the algoodoo site (www.algoodoo.com) you will find many examples of phun scenes
created by multiple people from all over the world.
When you build a phun scene is like you are building graphically a program where each
component you create have some physical properties attached because you need to draw these objects
it is almost like you are programming phun so this process of building a scene you are
actually programming phun and by extension a phun programmer is he who creates scenes.
Once you run the program and that you do by pressing play. You could have gravity act
on all the objects at once. It is actually very entertaining to see some of these scenes
created by other people. Even more fun to be able to create one of these scene by yourself.
Many of them are rockets, and tanks or small moving things. some other phun creators have
build ingeniously intricate mechanism. we are still in complete awe by some of the mechanical
things people have created with phun. Between those prolific creators I have found Livio
Zucca from Turin Italy I believe Livio's creations deserve more attention for his ingenuity and
mathematical flavor. Let me show a binary mechanical counter created by Livio.
The objective of this machine is to count the balls falling and collect the balls back
in an infinite counting loop. The main counting mechanism is a mechanical latch an electronic
latch is a circuit which has two stable states and thereby could store one bit of information
we can also create a mechanical latch and this acts similarly to a balance where the
pivoting point is reverse. The numbers in this case have dual function one is to inform
us of the state of the latch and also to act as stopper for the balancer. On the left side
we can see the ball feeding mechanism and the green bar with the slide inclination acts
as the collector of the balls rolling slowly towards the left. You may also appreciate
the mechanism for translating the circular motion into linear upward motion this mechanism
brings back memories of the mechanism that provided steam locomotive with motive power
in times past. An scene like this could be useful to learn about the binary numerical
system. That is a numerical system that uses only two digits and also used by digital computers.
Here is another version of the same but this time is got a mechanism that translate the
numbers from binary to decimal. This other version places balls in buckets
and the number of balls in each bucket correspond to the numbers in the fourth row of Pascal's
triangle That is 1, 4 , 6 , 4 , 1 One for example may also think about creating
machines that put balls on buckets. Livio got nice solutions for a machine that produces
the Fibonacci sequence! 1, 1, 2, 3, 5 Notice how the recursive equation f(n) = f(n-1)+f(n-2)
with f(1)=1 and f(2)=1 is executed mechanically with the use of balance that compare the weight
of the prior two buckets to the weight of the following bucket!
The sequence of triangular numbers is obtained by a similar procedure 1, 3, 6 , .. and also
the sequence of natural numbers 1, 2, 3, 4, ... a little bit harder is to obtain the sequence
of primes (prime numbers) using a mechanical mechanism. This mechanical mechanism simulates
the the ideas of sieve of Eratosthenes to obtain the sequence 2,3,5,7, and you may also
find simulations for pascaline a machine created by Blaise Pascal . Let me show last this wonderful
mechanical machine that is able to multiply two digits numbers and produce the result
in the decimal system. We believe Phun (Algooddo) will be a source of inspiration for students
and teachers. And it will be useful in the motivation and instruction of mathematics,
physics, computer science, mechanical engineering and electronic. Phun is opening a new universe
of interactive learning and should I dare say Fun. If you like to play or modify some
of the scenes displayed here visit our site blog.isallaboutmath.com for the links