Archive for the ‘trigonometry’ Category
A Zombie starts walking toward your house from 10 km away.
He walks in a straight line, but he is 5 degrees off target.
How far away from your house will he end up away from your house?
ZOMBIE LIKE PYTHAGORAS TOO!!!
WORK OUT HOW FAR ZOMBIE WALK.
The High -pot-in-use!
Everyone must know the HIGH-POT-IN-USE!
Meet Salman Khan. He has put free maths on-line.
This article on Salman appeared in The Sunday Times, UK, 12 JUN 2011.
Salman, 28, started putting tutes online for his 12-year-old niece, Nadia, and things grew. So far the Kahn Academy’s claim to fame are:
* Over 2,400 videos including hundreds and hundreds of 12-minute maths tutes
* Over 63,000,000 lessons delivered.
* Bill Gates kids use the site.
* A staff of 1 with funding from The Bill and Melinda Gates Foundation.
* Tutes on Biology, Chemistry and Physics too.
You can look up the maths tutes by topic @ The Khan Academy.
Or search topics on Youtube eg. Introduction to Conics Khan
Why Does Mathspig like The Kahn Academy? Because it’s:
Salman gives digital chalk-and-talk tutes like a teacher. He hand draws the equations and graphs. He uses a calculator from time to time, but he tends not to use whizz bang spreadsheet graphs or perfectly presented textbook equations. It’s a bit wobbly and it’s all coming from Salman’s head.
And students like this approach. It makes maths look do-able.
Mathspig thinks you are just GORGEOUS!!!!!!!!!
Australia’s Year 7 – 12 Maths Curriculum is already on-line and free, funded by McDonald’s. See What are maths teachers for, sir?
The tutes on Maths Online are produced by Aussie Maths teachers and they are very good. Mathspig, of course, imagined the quadratic function tutes might look something like this:
Mathspig went along to see the movie, ROBIN HOOD, starring Russell Crowe and Cate Blanchett. I was interested in the film for several reasons.
Firstly, Cate Blanchett went to the same primary school as Mathspig’s children in Melbourne. Such is our Aussie egalitarian attitude to education we do not single out past students for special attention. No picture of Cate Blanchett appeared at the school during Mathspig’s kids education and none, as far as I know, to date.
Secondly, I’m amused that two Australian stars featured in an American remake of a British classic tale. I was just a bit disappointed that Russell Crowe didn’t say something like ‘No worries, King John, mate!!!!
Another amusing aside was that the re-engineered history in this Ridley Scott tale meant Robin Hood had a great influence on British History. I am only too delighted to discover that Russell Crowe wrote the Magna Carta.
How Far Could Longbow Men shoot their Arrows?
I was very intrigued by how the long bowmen fired their arrows. Robin Hood begins the film as a long bowman called Robin Longstride. The film critic for the New Yorker suggested ‘Longstride’ was not the ideal name for Russell Crowe’s nuggetty Robin. I think Robin Chunky-Guy might be more appropriate.
When I did some research ( Longbow arrow speeds)I found that Russell Crowe’s build was closer to the original longbow men than earlier Robin Hoods such as the tall and rangy Errol Flynn (Shown). It is believed that longbow men of the era could draw -a force (on the bow string) of 150 lb-f (pound force) or 667 N (Newton), which is, at least, twice the draw force of bowmen today who, if they are good, can draw 60 – 80 lb-f or 267 – 356 N.
Longbow men used heavy wooden arrows and not the carbon shafts used by archers today. Arrow speeds are estimated for the longbows to be up to 310 f/s (foot per sec) or 100 m/sec.
In the film I noticed that Robin Hood – especially in one dramatic shot at the end, – aimed his arrow at a high angle in the air. ( See Below)
Mathspig believes you should always find the easiest way to do any calculation. so here is the EASY way. Assuming there is no wind or wobbly arrow movement we can split the arrow velocity into its horizontal and vertical components (Using vectors. If you haven’t done vectors just go along with it.) Then interesting things happen!!!!!!!!
We haven’t allowed for air resistance in the flight of the arrow so it would slow down….. BUT Russell Crowe … I mean ROBIN HOOD was right.AIM HIGH and your arrows go a long, long way!!!!!!! Of course, the straight arrow traveling at 100 m/sec would travel 1000 m in 10 seconds or 1 km!!!!!!
Mathspig finds this amazing.
Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Mum fed the prisoners. Dad’s car an old FC Holden, maroon and white with a pink door, was the police car. And the police phone sat in the kitchen.
Australia has a very strict gun laws today. Thank goodness. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against the fridge in the kitchen – without it’s 6-bullet magazine – in case my dad was called out to some police emergency.
There were a number of gun incidents in my childhood. One time my mum was cleaning the house. She usually put paper rubbish in her apron pocket and threw it at the end of the day into our combustion (wood-fired) stove. She forgot she had three .22 bullets in her pocket. It took some time for the bulletsto heat up.
My parents were in bed when bullets started exploding in the kitchen. The explosion blew off the hot plate and blew the ash door open covering our kitchen in grey ash. And it nearly gave my dad a heart attack. This was a typical story of my childhood and why I became a humour writer.
My Dad the Sharp Shooter My dad stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s distributor cap. Phht! Car go no more.
Sharp Shooter Maths
One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle. The MOA can also be used to define the target zone (circle).
I cannot show you a triangle with an angle of 1′ because it would have to be 100m long on one side and only 3cm tall or 100 yds long and approx 1 inch tall.
Needless to say, drawings are NOT to scale.
A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.
(See pics. )
As the distance away from the target increases the target zone circle area increases.
When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question ‘Would medals protect the wearer from a sharpshooter?’ Note: Mathspig has obscured the identities. This is a theoretical maths question.
Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.
The diameter of a standard military medal is 3.5 cm. Mathspig has drawn up a diagram with loosely packed medals.
Using Pythagorus Theorem we can calculate the distance ac and then by subtracting 2r (2 x radius of the medals) we end up with the diameter n of the target zone circle.
Even at 100m the sharpshooter is looking at a target zone circle with a radius of 0.46cm. That is less half cm!!!!!!! The target zone is less than the size of an American Quarter and about the size of an Australian 10 cent coin or a British Pound. This is very difficult.
At 100m the sharpshooter is doing well to hit target in a target zone circle of 2.91 cm.
At 200m the target zone circle radius is 5.81 cm.
So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.
Another way to look at the sharpshooter problem would be to calculate the MOA – or minute of angle- to get inside the target zone. Here are the calcs for 200m. Find WEB 2.0 Scientific Calculator handy here.
This song was given to me by Dr Michael Green General Manager, Innovation & Space Branch, from Department of Innovation, Industry, Science and Research. He sang the song following Mathspigs efforts at being Freddie Mercury (See Maths Song page right)
(Sung to tune of the French children’s song “Frere Jaque”)
Sine squared theta
Cos squared theta
Take these two
Take these two
Add them both together
Add them both together
They make one
They make one
GEEK MASTER CHALLENGE!!!
Of course, this equation is just Pythagoras’ theorem with the hypotenuse normalised to 1.
Pictures: Theatre on line #mce_temp_url# which hosts madmaths sessions shown (above) but unfortunately in French and ,um, in France. The madmaths geeks pictured are Soient Oliver Faliez and Kevin Lapin #mce_temp_url#