3 Ellipsoid Collipsoid

Maths-is-Awesome Activity

Ellipsoid Collipsoid

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.

Could you do this mathspiggies?

Make a conic section in 3D?

6. Mass Murderer or Maths Teacher?

Just to remind maths teachers to smile once in a while and in a NICE way, here are 12 pictures* : half are seriel killlers and the other half maths teachers.

But which are which?

What’s the probability of getting ALL answers correct?

Yes! 50%

Weird Maths Activity

Mass Murderer or Maths Teacher?

You choose!!!

Subject A

 

Subject B

 

Subject C

 

Subject D

 

Subject E

 

Subject F

 

Subject G

 

Subject H

 

Subject I

 

Subject J

Subject K

 

Subject L

 

This is a maths teacher,
However, you might understand why students suspect he falls in the other category!!!!!!

ANSWERS:

A. Teacher, B. Teacher, C. Jeffery Dahmer, D. Teacher, EDr Harold Shipman, F. Charles Manson, G. Albert Fish, H. Joseph Harwell, I. Teacher, J. Teacher, K. Teacher.

 

*All the teacher photos come from education archives but will be removed on request.

Barcode Maths

Here is standupmaths comic Matt Parker doing calculations in his head including a bar code calculation.

Thanks to Matt making the barcode calculations look EASY Mathspig spent about 12 hours blowing steam out her ears and tearing up packaging trying to get the barcode maths to work.

This is THE absolute best exercise to test accuracy in simple calculations including transcribing numbers, which are so easily misread. It also shows you how BARCODES work.

The cash register pings if the BARCODE CHECK DIGIT Algorithm matches the CHECK DIGIT, which is the last digit in the barcode. This is how the cash register computer checks that the data in the barcode has been transferred correctly. All data transfers have some sort of data check algorithm.

The PING is KING!!!!!!!!

Mathspigs, you can check your maths skills by picking up the nearest product with a 13-digit barcode and calculating the CHECK DIGIT. The answer is at the end of the barcode.

You can find an alternative explanation here.

If your calculations won’t work use the online CHECK DIGIT CALCULATOR (EAN 13). If it is right check your calculations again!!!!!!

The Hunger Games Maths

The Hunger Games is about MATHS. Here are some interesting Hunger Game statistics.

………………………………………………………………………………………….

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THE PLOT:

…………………………………………………………………………….

……………………………………………………………………………

In Suzanne Collin’s book, The Hunger Games, 12 districts in the land of Panem are suppressed and controlled by a vicious elite, who dress like neon-coloured French courtesans.

Each year the cruel rulers select one teen of each sex between the ages of 12 and 18 from each district to become tributes, who must fight to the death in a televised, sponsor-supported media event called The Hunger Games, set in a staged wilderness.

Only one tribute can survive. Katniss Everdeen and Peeta Mellark from the poor coal-mining District 12 are the local tributes for that year and must play at being star-crossed lovers to gain sponsor support and survive.

………….. 

…………………………………………………………………………..

THE MATHS:

…………………………………………………………………………..

……………………………………………….……..The Reaping…..

Tributes are selected in a process called The Reaping. The names of the, approximately, 2,000 young people in each district are placed in separate barrels for males and females and the names are drawn out of these barrels BUT…

……………………………….

12 year olds …….. 1 slip

13 year olds ……..  2 slips

14 year olds ……..  3 slips

15 year olds ……..  4 slips

16 year olds …….. 5 slips

17 year olds ……..  6 slips

18 year olds …….. 7 slips

……………………………………………………………………………………………………………….

…………………………………………………………………..

BUT you can gain extra ‘food’ if you accept for more name slips.

Gale Hawthorne (pictured above), Katnis’ friend from District 12, has 42 slips in the barrel. What are his chances?

We will assume that there are 1,000 teens of each sex in each district and an equal distribution – rounded off – for each age group to 1000/7 = 143

 

 

Age Group	Name slips	Total Name Slips	Probability of being REAPED	Probability P
12	1	143	1 : 4004	1: 4004
13	2	286	2 : 4004	1 : 2002
14	3	429	3 : 4004	1 : 1335
15	4	527	4 : 4004	1: 1001
16	5	715	5 : 4004	1 : 801
17	6	858	6 : 4004	1 : 667
18	7	1001	7 : 4004	1 : 572
total		4004

 

……………………………………………………….

……………………………………………………..

 

12 minute Maths Guru

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:

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.

Go, Salman.

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:

Easter Egg Maths

Mathspig can’t stop thinking about EASTER EGGS.

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How do you do you  graph  an Easter Egg?

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Fortunately, Jurgen Koller @ the fab mathematische-basteleien website has already solved the problem.

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Start with an Oval.

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To change it to an egg shape multiply  y or y² by  t(x), so that y becomes larger on the right side of the y-axis and smaller on the left side.

y(x=0) must not be changed. 

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The equation of the ellipse:

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e.g. x²/9+y²/4=1

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BECOMES

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x²/9+y²/4*t(x)=1.

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Three examples:

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Now plot in chocolate paint and eat graph. Yum!!!

According to Jurgen Koller, Don M. Jacobs, M.D, Daly City, USA developed a nice egg shape by changing the circle equation x²+y²=1 a little: x² + [1.4^x*1.6y]² = 1.

The egg equation is an exponential equation of type t3 above. This shows this conversion:

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Thanks, Jurgen. I wonder if he’s an Egghead!!!!!!

Every Day is Pi Day

Wowwwwwwwwww!!!!!!

π   π   π

Mathspig is very excited to note that Pi has been in the news this week.

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Firstly, in an article titled Pimp My Memory New Scientist, 2nd April, cited Chao Lu’s feat of remembering π to 67,890 places in November 2005.

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It took Chao (pictured below) 24 hours and 4 minutes to recite the 67,000plus places!!!!!!!!

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π

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If Mathspig was listening I dare say she would have fallen asleep and slammed her snout into the table top at 200kph at about the 300th decimal place.

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But I can’t help wondering what would happen if some one said, Aussie style ‘Nah, mate! You missed one. That 61, 235 place was a 3!!!!!’

π

This is more a feat of memory than maths.

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Wowwwwww !!!!^2!!!!

Then The New Yorker, 4th April 2011, reported on Pi Day activities in the Facing History School (pictured ), Hell’s Kitchen, NY. (Below random students)

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Maths teachers held a pi-memorisation day on Pi Day (3/14 in USA, which unfortunately in Australia is written 14/3) offering a new iPod Touch as a prize.

π

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There was also a pi pie-eating contest and a pi “jeopardy” game.  The Maths teachers all wore Pi Day teachers with names printed on the back such as Karina “The Algorithm” Garcia.

π

 

The winner of the pi-memorisation was a sophomore (Year 10 in Australia), Jason Gil, who recalled 162 digits. Yey!!! Go Jason.

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π

Mathspig urges maths teachers to have a fun maths day. Other subjects have days and events!!! Give maths a big profile in your school. A Pi Day is good. And a pi-memorisation challenge can be lots of fun. Here are three ways to remember Pi.

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π

1.Phone No. Method

π

Some students at Facing History School, NY committed  the pi sequence to memory by putting the numbers in blocks of cellphone numbers.

3.1415926535 8979323846 2643383279 5028841971

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π

2. Song Method

The Pi sequence can be remembered using a Pi Song.  Here’s a song to recall the first 10 digits.

π

If numbers had a heaven

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Their God would surely be

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3.1415

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92653

π

It is sung to the Mickey Mouse Club Song.

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Here is a more entertaining song called Mathematical Pi Song by 4ACT, which proves that good mathematicians make crap singers.

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3. Piem Method

The third way to memorise the pi sequence is to write a PIEM … or Pi Poem.

π

It can be a crazy poem but each word has the number of letters of the digit to be remembered.

π

eg.

How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics.

π

Here’s a piem by Maths pig:

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Get a grip u maths pyschopath I’m afraid piday fun shidz students painfully.

π

All right, already. Some poetic license is allowed. Tricks such as rhymes and mnemonics like the piem will only help memory if they are witty and apt but you must know what you can get away with.

π

How to study for exams? According to studies reported in New Scientist the best way to learn for an exam is to constantly test your memory. Make it work hard. REcall. REcall. REcall.

π

I’m Mathspig. I didn’t say I would be a nice pig.

Cool Formula For Calculating Skyscraper Sway

The world is in turmoil mathspigs with earthquakes, tsunamis and nuclear power plant meltdown worries. It is the job of engineers to calculate and incorporate – as far as possible- safety margins into the structures of buildings, dams and power plants. Observers have noted that the skyscrapers in Fukushima wobbled during the recent 8.9 magnitude earthquake in Japan.

This is intentional, as rigid structures can snap in strong winds or during earthquakes.

But the maths used to calculate SKYSCRAPER SWAY is straightforward.

The Earthquake Engineering website offers a simple explanation.

Short, rigid buildings are damaged in earthquakes because they shake very fast. 10 story buildings have a period of oscillation of about 1 second the same as the earthquake pulse. This is VERY dangerous.

Tall, flexible buildings can withstand an earthquake because they can sway. They are like a very large, slow moving tuning fork. If they are TOO RIGID they snap. If they are too flexible the people on the 100th floor would be throw all over the place.

The 59-story steel-construction Citicorp Centre, NY (pictured) has an oscillation time of 6.7 seconds. Details Google Books.

The 102-story brick clad Empire State Empire Building sways about 8cm ( 3 inches) whereas the 110-story steel -mesh World Trades Centre Towers, NY, before they collapsed swayed over 1 m ( 3 ft 5 inches).

One more thing. You want buildings to have springy foundations so they don’t snap at the base and fall over.

Earthquake Engineering

The idea is not to strengthen the building, but to reduce the earthquake generated seismic forces acting upon it. This can be done in 3 ways.

1. Base Isolation. Rubber pads or Rollers. Are used so the base does not feel the full shake or jump off foundations.

Details Base Isolation Specialists

2. Shock absorbers or dampers are added to the structure to dissipate the seismic shock.

Details Damper Supplier

3. Active Tuned Mass Dampers use a computer controlled counter moving weight to actively move against the building sway.

The 508m (1,667-foot) Taipei 101 Tower would sway back and forth up to 60cm (2 feet) each way within five seconds. This according to Wired magazine is highly barfogenic or spewdacious, perhaps, in Aussieland.

The Taipei 101 engineers included a 662 tonne (730-ton) counter giant pendulum to act as a counter weight.Some buildings use a big block of concrete.

It is pushed in the opposite direction to the building sway to dampen the oscillation.

Earthquake Engineering Maths

Take 1:

Wired magazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):

But I’m going to use a student friendly equation from Wind Engineering for Large Structures.

Mathspigs, you can just look at this equation and see how to change it to make a building EARTHQUAKE SAFE. Keep in mind that k, the stiffness constant actually decreases for taller buildings.

Imagine you are designing a building to withstand the 8.9 magnitude earthquake. You have already added base isolation. Now you have three options to work with: building mass (m), damping constant (c) and stiffness constant (k). Remember the earthquake force is constant. If you change just the stiffness of the building (k) what happens to the distance of sway(x)?

Engineers have to come up with the optimum design for the strongest structure with least acceleration (but enough building mass for strength), greatest damping and least sway at the lowest cost.

Earthquake Engineering Maths

Take 2:

Structural Engineer Ron Klemencic explained on the Discover News that a simple rule of thumb for calculating skyscraper sway was to simply divide the buildings height in by 500 because the building codes demand the building fit a 1:500 sway ratio.

The tallest building in the world at 2,716 feet (828m), the Burj Khalifa, Dubai, would sway back and forth about 5.5 feet or 1.7 m.

Ahhhhhhhhh!  But you would have to drag Mathspig onto the 168th floor screaming.

But mathspigs you can work out the sway on the top ten tall buildings in the world.

The 10 Dumbest Maths Questions

This post could be called the 10 Most Annoying Maths Questions. It began when Sarah Ebner, who runs the fabulous Edu Blog for the Times (UK) Schoolgate asked me to comment on her daughter’s maths homework.

Here is the question:

This week we have been working on addition and subtraction linked to money. The children have been using skills relating to mental strategies such as bridging through a multiple of 10, number bonds, partitioning, doubling and near doubles, counting on or back in 10s, using what they know to look at patterns or use the inverse, using imaginary number lines or 100 square in their heads. They have also been using the idea of the difference when doing some subtraction sums or when giving change

Homework task: 

Using the appropriate strategies, complete the attached worksheet. Show your workings. Buying a balloon. Lolla bought a balloon at the circus. She gave the clown six coins to pay for it.

What could Lolla have paid for the balloon? Which of your answers seems a reasonable amount to pay for a balloon?

Key questions: 

What is the largest amount of money we could make? What is the smallest amount of money we could make? How will we know when we have all the possibilities?”

Now keep in mind this HOMEWORK has been set for an 8 year old. The complexity of this maths is ASTOUNDING, obviously, for an 8 year old. This question fits the heading ‘Permutations & Combinations’ which introduces Statistics. The language is over-the-top. It is in Australia too. Why can’t kids just DO maths? I was helping my 10 year old neighbour do his maths homework on Thursday. He was doing short division. ‘You have to know the algorithm’ he explained. “You mean you have to know the way to do the maths?’ I asked. His 8 year old sister did a pig drawing for me. I think she’s captured the moment, really without prompting.

PARENTS who do not do maths must feel totally intimidated. As an ex-maths teacher married to an engineer our kids were not blessed either. We tried, on occasion, to help them out. But it was TOO MUCH information. It might explain why both of my children grew up to be arty. One of my kids was bored witless in maths and would fall asleep on his notes. The other one did maths like SUDOKU to fill in time between art classes. Their experience, in part, is why I’ve created Mathspig. They’re not alone. Australian students are dropping advanced maths in droves. The statistic shown was published in The Australian yesterday (20th March, 2010) 

I went and read a number of maths books lying around the house – collecting dust – and I found there was a real pattern to Dumb Questions.

When I returned to maths – as a hobby, always lerved it – after 25 years in the media I found texts books often read like THE ANCIENT RED SEA SCROLLS. What area does a goat graze???? A GOAT!!! Why not ‘what area does your computer mouse need to move at different lengths?’ Good maths students will tackle anything. Teachers face greater challenges. This blog is aimed at finding ways of grabbing the attention of ALL students.

Please send me any DUMB MATHS QUESTIONS you stumble across and I might give an award at the end of the year to the dumbest. The questions below are from a Year 7 TEXT book unless specified. It was quite a good text but well…..

Here are the 10 Dumbest Maths Questions;

1.SO FAKE

These are the questions where maths teachers (Text book writers are usually maths teachers) want to say ‘Look! See maths is important. You can use this particular maths to solve real problems. But the questions are so FAKE they’re laughable. Some boil down to the three men walked into a bar type model … others are just weird. Check out the Names in Q (below) and the Year 12 Q. What is the likelihood of hitting the bird? -Um, absurd!!!!!! 

2. ONLY AN IDIOT

Once again trying to show students that maths is useful questions are asked that only an idiot would try to solve using maths.

IN the Year 11 Q2  (Below) if you had any relationship with a sheep or a goat – I’m thinking goat farmer – you don’t calculate the area grazed. You move the goat. In Q1 how could your friend remember all of those details, but forget the actual number of your house!!!!!!

 

3. THE MORAL TO THIS MATHS

In the first question check out the punishment for not doing maths!! That’s about as subtle as being hit on the head with a Maths Landing Vehicle.

In the second question the mathematicians die!!!!! Mind you, the idea might cheer up the class. look how much homeowrk the kid does in the last Q? Year 7.

4.MAKE THE MATHS WAY MORE COMPLICATED

In the first Year 11 Q you do not use matrices to score cricket statistics. In the second Q if you want to know the names of your friends, um, ask them.

 

5. REIGN OF TERROR

or Fear and Loathing in the Loungeroom. This is when the maths set is way beyond the resources or standard of the students involved. If these questions are then sent home as homework – as with the Q that started this whole discussion – then the pain is transferred others. Sometimes you suspect that teachers offload the questions they can’t answer to parents!!!! Here are some more. The Q1  is doable but it will be hours of fun and games for all the family. Q2, um, Wha?

6. CLUELESS

The students are studying fractions, say. Then they are given a task that involves maths they have not learnt yet. The problem is that the question looks reasonable but isn’t. These sorts of questions produce the whining lament of young students … ‘I can’t do maths!!!’

7. WE ARE FUNNY GUYS. WE MATHEMATICIANS. HA! HA!

When maths teachers make jokes they are often lame. Check out the Question below. It’s just bad PR. Who would want to grow up to be such a nerd.

 

8. IMPOSSIBLE

Either the question is impossible to solve. These often come from typos like ‘find the square root -4′ in Year 8. Or the question is just all wrong. Could you cut a cloth into 1mm strips…. without a laser cutter?

 

9. WHY BOTHER?

There is no point to doing the question. Who would count the legs to find out how many beetles are involved? So why do it?

 

You could go to all the trouble to work out the surface area of your dog and then calculate how many hairs Rufus had, but why? Is Rufus worried he’s going bald?

10. THERE’S NO ANSWER YOU B*&#*#!S

This has made me rethink mathspig. I’ll add more answers. There is nothing more frustrating that doing all the hard work and there is no answer at the back of the book. You want to throw the book at them. The following is a Year 12 Q but, alas, no answers at the back of the book. 

10 You can out run a lava flow

Every volcano disaster movie from Volcano (1997) with Tommy Lee Jones to Dante’s Peak (1997) with Pierce Brosnan someone somewhere tries to out run a lava flow. Is this possible?

The answer is maybe. You will find everything you want to know about lava flows @ http://volcano.oregonstate.edu/

 On January 10,1977, at Nyiragongo lava sprang from the sides of the volcano moving at speeds up to 40 miles per hour (60 km/hr). About 70 people were killed.

 Measuring the temperature of lava. Photograph by R.L. Christiansen, U.S. Geological Survey, January 9, 1973.
The fastest Lava flows recorded were in Hawaiiin 1950 when Mauna Loa erupted. The lava traveled at 6 miles (10 kilometers) per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 60 km/hour (97 kph).

Speed of average sprinter = 19 – 24 kph

Can you out run lava?

Work it out mathspigs. You are 300m ahead of the lava flow and you need to get up a hill to escape, which is 1000m away. The lava is flowing at 30 kph and you are running at 18 kph.

Will you make it??????