Skill: Geometry, scale, ratio, conic sections, ellipses, parabolas, hyperbolas and more.
Level: Senior School
Senior maths students are busy, mathspiggies. But insipration energises.
Mathspig was amaaaaaazed by these cardboard models were made by Martin Schilling because he made them in 1901. This was long before computers made the job easier. More info here.This is what a car looked like in 1901.
If Martin Schilling could make these Conic Sections, so can any senior student. You will find Conic Section diagrams and equations here.
Brazilian architect Carlos Teixeira created an incredible labyrinth made entirely from layered recycled cardboard for the 29th International Biennial in Sao Paulo.
Labyrinths are mysterious. And mathspiggies, look at that lovely parabola. Making a labyrinth on this =scale may be beyond the resources of a maths class … but then again some imagination and some maths skills and voila:
In phase one of the project 240 students at Kingsford Primary School in Aberdeen used interconnecting materials to design and build a labyrinth inspired by the story of Icarus.
Today we are going to be Food Scientists; food science needs maths and this food science is important for your health and diet.
Before we do the maths we must understand the science of sugar. Here is a simple explanation.
In the USA corn, which is 100% glucose, undergoes an industrial process that breaks down the long glucose chains and converts some glucose to fructose because fructose delivers a bigger sweetness hit on your tongue and corn is cheap. The resulting HFCS (high fructose corn syrup) is, on average, 60% fructose.
Now we can do the maths.
This important information below comes from the Goran Labs
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Food Science Maths
or
Fast Food Maths
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1. Draw up a bar graph of the weight of sugar(sucrose) and fructose for 8 drinks.
2. Plot the weight of sugar(sucrose) and fructose for 8 drinks on axes.
3. Assuming that 100ml of soft drink weighs 100g – this is realistic- calculate the percentage of sugar(sucrose) and fructose. This exercise is to see if students are paying attention. It is very easy!
4. Drinking too much sugar in any form is not advisable, but fructose in large quantities just adds calories without satisfying your hunger. Which drinks are loaded with fructose?
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:
Scientists, bless their little cotton sox, are always trying to calculate the funniness of a joke.
Jokes depend on the person, their mood and a zillion other factors. We’d say there are TOO MANY VARIABLES in maths. For instance, context rules. Titanic jokes don’t go down well on a sinking ship.
Note: y = 0 for no reaction and therefore funniness index is zero.
y < 0 for a frown make the funniness index negative.
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GOOGLE FUNNINESS ALGORITHM
Google created a funniness algorithm to rank funny videos in the You Tube Comedy Slam. The algorithm scores for views, comments (Funny, hilarious etc), laughter sounds (hahaha), web acronyms ( lol, lmao, rofl), (c) funny, emoticons , and repeats (lololololol, loooooooool )
And the winner is: NO NO NO CAT
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FUNNINESS MATHS EXERCISE
or the DAD-Joke-O-Meter
Dads, Uncles and Some Teachers tell really dumb jokes. Dumb jokes are called Dad Jokes.
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.
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How heavy is $500,000 dollars?
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and repeats (lololololol, loooooooool )
