Maths doesn't have all the answers

Many people (including maths teachers) assume maths has the answer to life the universe and everything. (The answer is 42 - Click here to find out why!).

In particular maths has the answer to "how do i make the most money?". Here is an example.

Drinks companies - Coke, Pepsi, Schweppes etc. - are big business. Their aim is (understandably) to make as much money (profit) as possible.

Therefore - you would think - they would design the cans their drinks come in to be as cheap as possible, to make more money.

To make a can as cheap as possible, you need to use as little metal as possible. This means that for a fixed Volume of 330 ml, you need to reduce the Surface Area to as low a number as possible.

Whilst this sounds complicated, the picture below is the working for this problem, as done in class with Y12 mathematicians.

As you can see, the radius of the can should be 3.74 cm and the height should be 7.48 cm. (NB - the Diameter and the Height are the same, is that coincidence). Compare this to a real can. If the maths says a can should be a certain size why are they not - the company could make more profit (by making cheaper cans).

So - your thoughts please - why do they not make the cans this size? The answer is in work you may do in Tech lessons...

Get the App....

You can now download an app (for Android only at the moment), that makes it easier to view the blog on your Android device.

This app is really just an experiment in app creation, so all comments really are appreciated.

SmartPhone Apps for Learning

Whilst you are (rightly) not allowed your phones out in school, unless your teacher specifically tells you that you can use it, there are a number of apps you can download (free) from the android market place that can help support learning.

Yes, this is android specific, but many of these apps are also available for apple, be it ipad, iPhone or iPod touch.

Evernote is one of the most general purpose. Keep notes, photos, voice memos organised, and tagged. It has the advantage that all notes stay synchronised across all devices. This means my notes are on my phone, my iPod touch, and my school laptop. I can also access than by logging on to their web site from any other computer. Some students have used this to take pictures of exam question s that they struggled with, using the photo as simply writing about a graph question is less effective. The picture is taken from a y11 learning journal, and shows how it can be used (click to enlarge).

Algeo is a graph drawer / calculator. Whilst there is no substitute for your own scientific calculator, if you are plotting or sketching a graph it can be useful to double check the shape. It only draws graphs in radians, so don't forget to double check. For things that don't involve sin / cos / tan, however, it is very simple to use.

Dropbox is also general purpose, and replaces the need for a usb memory stick that is too easy to lose. It's a free online 2Gb storage space. Like Evernote it synchs between web browser, PC download, and Android / Apple download, but instead of notes, it is files of any sort. This means you can work on a document at home, and upload to dropbox when done. You can download to your mobile device if you want to check it, or you can access it through the web at school, or on any pc. It also allows the sharing of files between users, although this is not something I've tried.

Triangle Solver is a simple triangle solver. Type in any three bits of information from the six about any triangle (3 sides, 3 angles) and it calculates the other three using Sine / Cosine rule. It also copes admirably with the case with 2 possible solutions.

Solver, on the other hand, uses the quadratic formula to solve quadratic equations - again, useful for checking answers. Bad news (for most students) if you have an equation that doesn't really have any solutions, you will get a funny complex answer which involves the number i. Sixth form further mathematicians - good news - if you have quadratic with no real solutions, it will give you complex ones!

Wolfram alpha is not a free app, but the mobile website is free. Anyone who has seen it in action knows how powerful it is. If you haven;t then go play! Wolfradroid is a free app, which allows you to speak your entry to W|A!

One last one - Shush! IT allows yuo to put your phone on silent, but decide what time it should become noisy again! Perfect for school. Silent (and in the bottom of your bag) at 08:30, but automatically coming on again at 15:30 for home time. I use it all the time.

So, who has used any of these apps - how have they supported your leaning? What other apps are out there for android that will help your maths, or your learning more generally.

Who uses apple? What ipod touch / iphone apps would you recommend? Who wants to write a blog post on apple apps to support learning? Email the usual address, or come and find me at school.

Published by Mr Smy.