Here is LAGA Phd student Attouchi @ the 13e Salon Culture & Jeux Mathematique in Paris.
She was showing students how to use a graph to create anamorphic projections. This is interesting maths!!!
Here is an anamophic projection painted by extraordinary Australian artist Juan Ford. Mathspig went to Juan’s amorphic projection show. Now that I’ve tried to do one by hand, I have more respect. It’s totally tricky, but doable.
You will find more of his anamorphic projections @ artabase
Conformal Mapping
In maths we call this type of image distortion CONFORMAL MAPPING.
Mathematicians write equations for conformal mapping, which means they produce equations that can turn your picture into an image you might see reflected in a fun park mirror or even in pond ripples.
Here are some images created by Wei Zeng, Lok Ming Lui, Xianfeng Gu, Tony Chan and Shing-Tung Yau who, as mathematicians would say, create Quasiconformal Maps Using Discrete Curvature Flow. You’ll find more here.
Here is the mapping graph used by Attouchi to create Anamorphic Projections.
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All you need is this grid (Download pdf file here Anamorphose Cylindrique) and a cardboard tube ( Diam 47mm or a little bigger than a toilet roll tube) covered in shiny silver paper (as used in He balloons or use gift wrap paper.)
You can just see the dotted line indicating where to place the tube mirror on the grid.
But don’t be mislead. Creating anamorphic projections is really tricky. Mathspig nearly blew a fuse trying to do a drawing. In the end I decided to keep it simple and use letters. Students could start with a triangle or their name. Keep it simple mathpiggies!!!!!! But it is such fun.
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Ooops! Mathspig forgot to write Maths 4 Eva as a mirror image. Take 2:
Mathspig noticed in the film that Katniss was aiming the arrow directly at the target. This is a problem. Arrows drop under gravity. If Katniss aims directly at the target she will hit it below her aim point. To overcome this she must raise her arrow aim.
What angle should she choose?
Robin Hood used a long bow and in the film Robin Hood archers raised their bows at a very high angle to cover long distances. See the diagrams below from Robin Hood Give Us Your Best Shot
According to The Flaming Arrow the speed of a modern arrow is 100 m/sec with a 65 lb draw weight.
Mathspig believes in using the SIMPLEST maths solution. In this case, very short arrow flight times are involved.
So we will assume the arrow velocity (Va) equals horizontal vector speed (Vx). This is an approximation that makes the maths sweet. Such an approximation might work for the arow flight in the first diagram (above), but not in the second.
First, mathspigs, we’ll calculate the arrow flight time to a target 100m away and then we will calculate the distance the arrow would drop vertically in that time as this will tell us the point in the air where Katniss should aim.
NB: An arrow will drop 4.9m over 100m to the target. In other words, Katniss would miss a human completely if she did not allow for gravity. Experienced archers automatically make this adjustment to their aim.
Or search topics on Youtube eg. Introduction to Conics Khan
Why Does Mathspig like The Kahn Academy? Because it’s:
1. Free.
2. Quick
3. Clear
4. Low-key
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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.
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:
The Millennium Bridge a suspension footbridge across the Thames River in the heart of London costing $Aus 32 million opened on 10th June 2000. It closed half an hour later as pedestrians were being knocked off their feet by the swaying bridge.
The Maths Error: Designing 3D Bridge in 2D.
The three big mistakes, often catastrophic, in engineering are maths, materials or human error (ie. Hitting the pylon of a bridge with a ship. Tasman Bridge Collapse Hobart.. 1975). The Millennium Bridge was a maths problem. The bridge was designed in 2D. The engineers allowed for up and down movement but not sideways movement. Any kid running across suspension bridge in a playground knows that as you run it wobbles sideways! The bridge’s movements were caused by a ‘positive feedback’ phenomenon, known as Synchronous Lateral Excitation or wobbles. It cost $Aus 9 million to dampen the bridge wobble.
A similar maths problem with suspension bridge design involves harmonics. If the wind keeps adding an extra nudge each time the bridge sways and the bridge has not been designed to dampen this effect it can break apart. (See Galloping Gertie. 1940 Bridge Tacoma Narrows Bridge Collapse. Watch for guy who saves dog from car. )
Here are two links about graphs suitable for Year 7 mathspigs.
The first will link you to the most dreadful song you are ever likely to hear about plotting co-ordinates on X and Y axes. The reason Mathspig is including this link is because it can be used by maths teachers as a threat.
If you do not work on your maths problems involving co-ordinates I will sing this song. (Insert Maniacal Laugh Here) Ha! Ha!
Spaceships Online Game:
