Passy's World of Mathematics

Circumference

Posted on August 21, 2011 by Passy

Image Source: http://upload.wikimedia.org

Drums are one of the most marvelous use of circles that we’ve ever heard of here at Passy World. So let’s get right into the beat of the Circle with a catchy Circles Song from Learning Upgrade website.

[youtube=http://www.youtube.com/watch?v=eiHWHT_8WrE&w=540&h=433]

Here is another great circles tune, this time by Maths Teacher extraordinaire: Mr Dave Johnson:

[youtube=http://www.youtube.com/watch?v=fogehnFNDw0&w=540&h=433]

So let’s start taking a deeper look into the mathematics of circles. We shall start with the distance around a circle. This is the circle’s “Perimeter”, and is given the special name of “Circumference”.

Image Source: http://files.abovetopsecret.com

Here is a video all about the Circumference of any Circle:

[youtube=http://www.youtube.com/watch?v=1XFkAZW-rWg&w=540&h=433]

Circumference Formula

The Formula for finding the circumference “C” is:

C = Pi x Diameter or C = 2 x Pi x Radius

We choose which formula to use depending on whether the math question supplies us with Diameter, or with Radius.

Diameter is the distance all the way across a circle.

Radius is the distance from the center to the edge of a circle.

Radius = 1/2 of the Diameter.

Here is a video about how we can work backwards from the Circumference, to find out the radius of the circle:

[youtube=http://www.youtube.com/watch?v=1-D_z9GatbU&w=540&h=433]

The Value of Pi

A really important part of working on Circles and spheres is the value of Pi.

Image Source: http://timthefoolman.files.wordpress.com

Pi is a mathematical constant whose value is the ratio of any circle’s circumference to its diameter.

Pi = c divided by d.

The most common value used for Pi is 3.14 or 22/7.

How the Pi Number is Determined

An estimation of Pi can be determined by drawing several circles of different sizes, and then measuring their circumferences by running a piece of string around the edge of each circle. We also need to use a ruler to measure the diameter of each circle.

For each circle, we then calculate Circumference divided by Diameter.

Here is a 3 minute YouTube video where Pi is accurately calculated using real pies.

The exact value of Pi is best calculated using a computer program, and it has lots of decimals in the answer, that extend endlessly into the billions.

For example Pi rounded off to fifty decimal places is :

3.14159265358979323846264338327950288419716939937510

To read about the fascinating history of Pi, click the link below:

http://ualr.edu/lasmoller/pi.html

Reciting of Pi

Various people reciting Pi as fast as they can on You Tube take their own world records very seriously. The one to beat is how long to recite the first 100 digits of the never ending decimals PI value.

A guy called Matt Parker originally set a World Record for reciting the first 100 digits. Then Michael J Lavery beat Matt’s record, and pegged the time back to 25 seconds:

[youtube=http://www.youtube.com/watch?v=vtBjxySCca8&w=540&h=325]

But Matt in true competitive spirit regained his world record back again with a much improved effort of just under 14 seconds. Unfortunately the YouTube video for this no longer exists.

The fastest Pi recital time, that Passy World has managed to locate on YouTube at the moment is by Rich Welling fom New York with a time of 13.89 seconds.

[youtube http://www.youtube.com/watch?v=K2hJNfXhhPw&w=540&h=435]
Finally, a very interesting video about a contender for the supreme Pi record of reciting it from memory to thousands and thousands of decimal places !

[youtube=http://www.youtube.com/watch?v=nsVyknWU7ak&w=540&h=433]

Circumference Games

Try this fun basketball game. The Coach will give you a lesson all about Circumference, that you can skip past, and then when you get questions correct, you get basketball shots. Note that to enter your player name, you have to click the mouse into the name box first.

Also when shooting, make sure you mouse click and hold down on your player until he is in the air and then release. If he is not off the ground, he will always miss the shot.

http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw41551

Circumference Tests

Math Goodies has an online test you can do at the link below:

http://www.mathgoodies.com/lessons/vol2/circum_part3.html

Click the link, and then scroll down the page and do this 8 question test on Circumference.

http://www.algebra4children.com/circumference-of-circle.html

Interesting Circles

Posted on August 20, 2011 by Passy

Image Source: http://www.fragilekitty.com/img/blog/pi.jpg

Circles are quite useful when we go skateboarding, and are called “pipes” and “half pipes”.

Here is a quick video of some Skateboarding inside a pipe.

[youtube=http://www.youtube.com/watch?v=7HUYo7lhwUE&w=540&h=433]

Here is some more skating inside a pipe, but this time with an awesome full circle loop at the end.

[youtube=http://www.youtube.com/watch?v=BDla-x-l4Hc&w=540&h=433]

In Skate Boarding, and BMX Bike riding, doing a full rollercoaster style loop is called doing a “Loop of Death”, (for reasons that will become apparent a bit later on).

Here is a video of two skateboarders making it around the full circle “Loop of Death”:

[youtube=http://www.youtube.com/watch?v=J2r_nhS6GNw&w=540&h=433]

But before you think about trying this at home, perhaps you should check out this video:

[youtube=http://www.youtube.com/watch?v=2ZLUZl8sdgY&w=540&h=433]

BMX bikes and Motorbikes have done some successful full circle Loops.

Speaking of things going round and round, here is an interesting little science experiment. (Warning: Don’t try this at home!)

[youtube http://www.youtube.com/watch?v=D9Qoff9e9R0]

So we’ve seen skateboards and bikes do full circle loops, but what about something bigger, like a car?

Here is a failed attempt to have a Car do a full circle Loop:

[youtube=http://www.youtube.com/watch?v=G6TLRpFvg7w&w=540&h=433]

Here is the mathematics of a Loop the Loop, which helps explain why it is so hard to do successfully.

[youtube=http://www.youtube.com/watch?v=9Ff8BR00EGc&w=540&h=333]

Here is “Fifth Gear’s” Loop the Loop high quality video of a car successfully making it. It gives the math that was used as well. In fact they set a new world record doing it.

[youtube=http://www.youtube.com/watch?v=wiZoVAZGgsw&w=540&h=435]

Now for something completely mad involving circles that happens in England at Gloucestershire every year.

This one involves a big round circular cheese being rolled down an insanely steep hill, with the competitors chasing it downhill at full speed.

[youtube=http://www.youtube.com/watch?v=OpzEF0D2xfE&w=540&h=433]

Well I’m feeling quite dizzy after that final round of circles.

My Virtual Home

Posted on August 20, 2011 by Passy

speccy red bedroom Image Source: http://3.bp.blogspot.com “My Virtual Home” is Free downloadable software for making 3D Home Designs. It is great fun to use, but requires a reasonable computer, and a good internet connection. Here at Passy World we downloaded and tried it out, with a view to it being useful for students doing house plan Perimeter and Area type maths assignments. Click the following links for some typical example assignments. http://its.guilford.k12.nc.us/webquests/areaperim/areaperim.htm http://schools.nyc.gov/offices/teachlearn/documents/standards/math/es/67dream.html Using a modern design program on computer like “My Virtual Home” is an engaging and enjoyable way of doing these types of assignments. It would certainly be a more fun, and better learning, than using the traditional ruler, colored pencils,and grid paper. Here is an Intro Video about the My Virtual Home program. [youtube http://www.youtube.com/watch?v=wp8dFe_2p9M] YouTube URL: http://www.youtube.com/watch?v=wp8dFe_2p9M Here is another Intro Video that goes for three minutes. [youtube http://www.youtube.com/watch?v=b06Nh02Of_k] YouTube URL: http://www.youtube.com/watch?v=b06Nh02Of_k This video shows how to Navigate around in My Virtual Homes. [youtube http://www.youtube.com/watch?v=hP6GlhPJwJo] YouTube URL: http://www.youtube.com/watch?v=hP6GlhPJwJo Here is a demonstration of Changing channels in MyVirtualHome. These are like different libraries that can be used while making your home. The “Better Homes and Gardens” channel is more focused on outdoor garden design, and the Building channel appears to be for making houses. [youtube http://www.youtube.com/watch?v=WdNLGacHR44] YouTube URL: http://www.youtube.com/watch?v=WdNLGacHR44 Here is a video on How to Display Measurements onto floor plans. This is what we need students to do before taking screen shots for their assignments. [youtube http://www.youtube.com/watch?v=p4cC85tZpqI] YouTube URL: http://www.youtube.com/watch?v=p4cC85tZpqI This video shows how to use the program Menus. [youtube http://www.youtube.com/watch?v=mfe73REzqew] YouTube URL: http://www.youtube.com/watch?v=mfe73REzqew Here is a walk through (has no sound) of a completed home. [youtube http://www.youtube.com/watch?v=hETqJrYQ5g0] YouTube URL: http://www.youtube.com/watch?v=hETqJrYQ5g0 Downloading the Program This is easily done by clicking the “Download” button on the following site: http://www.myvirtualhome.com.au/ As soon as the program is started for the first time, it is necessary to Register your details by giving a valid email address that a verification email can be sent to with a link that needs to be clicked. You can however use the program for three times before needing to verify it. The program has to download all the components for given houses from the Internet, and this can be up to 150Meg or more of data for a large home that is already furnished. The System Requirements state that at least a 128M 3D graphics card is needed. The PC we tried it on had an old NVidia gaming card in it, with an AMD Quadcore processor, and it was reasonable quality, but not quite 100%. It was okay while moving through the house, but angled lines were slightly jagged whenever we stopped moving. We are not sure how this program would run on a school laptop, but expect that it might be a little bit glitchy in the display. There could also be slow download times for components, depending on how good the school’s wi fi network is. Here is a screen print a house plan with measurements shown from our PC: Here is a screen shot of the walk through view of these rooms: My Virtual Home is a really well made fun program, and is great for designing houses and trying out different floor plans. It would be great for students to use for doing part of a typical Areas and Perimeters House Plan assignment at home, but we are not sure how it would go on the laptops at our particular school. We would need to get the program installed in a computer lab that has reasonable machines, but it would be painful to register each install and give each PC a password. We have emailed My Virtual Home to find out if educational institutions are using the program, and if there a free site version available without passwords that is easier to install and manage. Pending a response, we will update this blog post. Related Items Perimeter Circumference Area of Simple Shapes Area of a Circle Interesting Circles Composite Areas Measurement Formulas Tall Buildings and Huge Water Dam If you enjoyed this post, why not get a free subscription to our website. You can then receive notifications of new pages directly to your email address. Just find the subscribe area on the right hand sidebar, fill in your email address and click the “Subscribe” button. To find out exactly how free subscription works, click the following link: How Free Subscription Works Enjoy, Passy ]]>