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The following maths is suitable for Year 9+
but can be presented to lower grades just to show
maths is cool!
Archive for the ‘trigonometry’ Category
Hair Maths 1: The curly problem with curly hair
May 6, 2015
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More about Troy’s $million hair here. Hair statistics including how many hairs a human has on their head here.
Mathspig studied hair chemistry at uni. Tricky stuff. Put simply, hair is made of long strands of protein called keratin held together by sulphur (and some hydrogen) bonds. To curl hair, the keratin strands in the outer curve of each hair has to be stretched with curling tongs or hair curlers, heated and dried. The bonds in each hair reform with one side longer than the other … Hence, the hair curls like gift-wrap ribbon. But high humidity allows hair to reabsorb water and straightened hair just goes psycho curly again!
This excellent hair diagram comes from The Chemistry of Shampoo and Conditioner, in an article by EMMA Dux for the Royal Australian Chemical Institute
Some people are born with hair follicles that produce keratin at different rates across the follicle. They have curly hair. Hair perms chemically break and reform the sulphur bonds while the hair is held in small curlers (curly hair) or a very big curlers(relatively straight hair.) thus permanently curling the hair.
Here’s the Maths:
Curly hair looks like a 3D Helix.
More on 3D helix maths here
But, in fact, one strand of curled hair looks more like a spiral staircase.
The outer edge of the staircase is longer than the inner edge.
More helix maths here.
CHALLENGE:
Mathspig doesn’t expect Middle School students to plot a 3D Helix. But if they have started TRIGONOMETRY then they can see that the maths they are studying is used in CGIs for films and computer games in this case to generate realistic curly hair!!!! That’s cool. This maths was needed to model Merida’s curly hair in BRAVE.
SMARTY PANTS CHALLENGE:
Some middle school students could calculate some points on the helix.
Now students must be introduced to radians.
Simple EXPLANATION: Angles eg. 300 are not useful in calculations but fractions are very useful.
Eg. The circumference of a circle:
C = 2πr
Now imagine if you scan with a floodlight set at a radius of 1 km. So:
C = 2π
So the circumference is 2π.
You scan ¼ of a circle, the distance the light moves is ¼(2π)
or ½ π or 1.57 km (see below)
This measurement of an angle is in RADIANS.
00 = 0 circle = 0
450 = 1/8 circle = 2π/ 8 = 2 (3.14) /8 = 0. 79
900 = 1/4 circle = ½ π = ½ (3.14) = 1.57
1350 = 3/8 circle = ¾ π = ¾ (3.14) = 2.36
1800= 1/2 circle = π = 3.14
2250 = 5/8 circle = 5/4 π = 5/4(3.14) = 3.93
2700 = 3/4 circle = 3/2 π = 4.71
3150 = 7/8 circle = 7/4 π = 7/4 (3.14) = 5.50
3600 = 1 circle = 2π = 6.28
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You will find Cos tables at NASA Sine tables at Mathhelp
Answer here: Answers- 3D Helix Table
Advanced students may want to look at what the Uber Geek 3D Helix generating program at the free graph website PLOTLY here.
3. STUNTMAN MATHS: Motorbike Jump
August 19, 2014Star Stuntmen
Star Stuntmen Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”
Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman
Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.
His injuries are legendary:
More Evel Knievel
Ramp Design
The angle of the kicker in ramp design can vary from 100 – 700 (See below)
Moto-X Ramp Jump Maths
As any bike nut knows increasing speed and angle of take off will increase jump distance.
Here is a graph from final gear for speed vs angle to jump 90m.
METHOD 1 is approximate (See STEP 1 & STEP 2 above), but as METHOD 2 produces the same ans (See above), it is very useful.
You will find a thoroughly detailed calc for STUNT JUMP MATHS here:
And everything you ever wanted to know about PHYSICS OF STUNT JUMPS here.
Outdoor Maths Adventures: Middle School
June 30, 2014
Lego Man soccer fields will vary in size depending on the height of each player picked by each student. This does your head in. It is really challenging maths!
McGill Uni link here.
Don’t forget to throw in Mathspig’s lame protractor jokes.
You’ll find full calculations at the Maths is Fun blog.
You’ll find more fab outdoor junior and middle school maths activities at the terrific Maths and Movement blog.
Some students will discover their co-ordinate point is not on the grid. Students should then work out that they will need a different scale for the y-axis. You can get more inspiration at the Stand Again blog.
3. Find a Ghost Ship
October 14, 2013
The Ghost Ship, Orlova, disappeared on 4 FEB, 2013 while being towed off the coast of Canada and has not been seen since. The 1,500 tonne 110 passenger Russian vessel is drifting somewhere in the Atlantic Ocean. Missing, Richard Fisher, New Scientist, 5 Oct 2013
The Lydbov ORLOVA in action.
The Lydbov ORLOVA as a Ghost Ship.
Despite 2 separate SOS broadcasts from Orlova life rafts in March,
it has not been found. These SOS signals are the last two ‘sightings’ shown on the map (below),
but an aerial search did not find the GHOST SHIP.
Map from quofataferant.com
The Problem:
Ghost ships, pirates and illegal fishing vessels do not want to be found. They do not give off radio signals or identify themselves in any way to other vessels. Ghosts ships, in particular, are dangerous because other ships can crash into them at night. Seven ghosts ships have been found since 2000 including an 80m tanker off the coast of Australia.
GPS is not always accurate. (Scroll down to see error chart: 10. Design Cool Techno Stuff )
Ships must use radar to get instant readings of other vessels in the shipping lane. Can you find a GHOST SHIP Mathspiggies?
Radar BASICS:
Radar, short for “Radio Detection And Ranging”, sends out short pulse microwave beams that either focus on a narrow area (eg. speed cameras) or scan an entire semi-circular dome (eg War ships). Radar measures the angle and time taken of the reflected echo. This gives the location and altitude (distance and angle) of the airplane or ship.
It is used to detect the location, speed and direction of weather fronts, cars, airplanes, ships and more.
The weather radar beam is typically reaches about 322km or 200 miles. Here is the current radar map produced by the Bureau of Meteorology at the Terry Hills unit north of Sydney (pictured below)
- Bureau of Met RADAR
with protective dome
The Doppler Effect is used to calculate the speed of the ship. Every kid knows the Doppler Effect. eg. sound of a racing car turning a corner. High pitch approaching, low pitch leaving as sound waves are shorted on approach and lengthened on departure. Today Doppler Radar is automated. This was not possible before computers. eg. World War 2
The Maths:
You are going to do some World War II Radar Operator maths.
To do RADAR MATHS you must THINK HARD and picture what is happening in your mind. All you see on the screen at any one time is YOUR SHIP’S POSITION (in the middle) and a BLIP showing the GHOST SHIP’S POSTION as the microwave beam scans the ocean.
You mark the GHOST SHIP POSITION on screen and then do these calculations. But remember this …every time you see a blip you have moved too.
Now we’re going to look at the sort of calculation needed if ships we’re heading on a collision course. You will find all the GHOST SHIP DATA under the RADAR screen (below).
10. Way Weird Maths
January 15, 2013In the Way Weird Maths department are:
1. The Back Hair Coiff
2. The Fibonacci Hair Flip
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fibonacci hair
3. Fractal Jewellery
This jewellery made with diamonds and sapphires by Mark Newson for the jeweller Boucheron is based on the Julia Set shown below.
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Julia Set
4. Scary Math
Halloween or not, this guy is scary!!!!!
Could this be the math teacher you do not want to meet int he dark?
6. Geometric Hair
Mathspig calls this the Isosceles coiff (below). You have to see it from the Right Angle!!!
The Cubic Hair. The model is actually saying ‘Geometry stole my brain’.
The Tesselation tresses. The hard work is is walking into the wind so you don’t upset the tessellations.
7. Maths bling watch
Hammacher Schlemmer is offering The LED Matrix Watch for $79.9
How do you tell the time? Work it out mathspigs.
8. Maths is Evil Mug
See, maths is evil. We have the proof!!!
9. Math Body Art
These are scary maths tatts. What if the tattooist failed maths? He might make a big mistake. And you’d have maths teachers forever correcting your back … possibly with red pens.
….You wanna punch in the face by an inverse function
………… I am the unit circle of an exponential cult!!!
