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Did Einstein Really Flunk at Math?

May21

In this picture, taken in 1934, a rather nervous-looking Albert Einstein gives a lecture to the American Association for the Advancement of Science in Pittsburgh. But, rumour has it that he failed in his early math exams.

Scientists announced in 2016 that they had detected gravitational waves from the merging of two black holes in deep space — something predicted a century ago by Albert Einstein’s General Theory of Relativity.

The finding serves to underscore — again — the prodigious genius of Einstein, a theoretical physicist whose work fundamentally changed the way humans view and understand their world.

He was born in Germany in 1879, worked as a patent clerk in Bern, Switzerland, starting in 1905, and in 1915 completed the earth-shattering General Theory of Relativity, which helped explain how space, time and gravity interact and propelled him into the scientific stratosphere. He immigrated to the United States in 1933 and spent the rest of his professional career at the Institute for Advanced Study in Princeton, N.J., remaining active in science as well as political and social issues until his death in 1955.

There are also commonly held aspects of his childhood and education that seem to conflict with the broad genius that he was. That he was a lazy child. That he was a bad student who flunked math. That he had a learning disability. How much of this is true?

According to various sources, including the Albert Einstein Archives in Israel, which has the largest collection of Einstein papers in the world, some of that is true and some isn’t.

Did he start talking late? He told a biographer, Carl Seelig, that his parents “worried because I started to talk comparatively late and they consulted a doctor about it.” Yet his grandparents wrote a letter to family members after seeing him when he was 2-years-old and did not mention any such delay, instead noting that he had “droll ideas.”

Was he a bad student? He started school at 6½ and, according to an Albert Einstein Archives biography, his early teachers did not find him especially talented even though  he got high marks. He hated the strict protocols  followed by teachers and rote learning demanded of students, which explains his disdain for school, which he carried with him when, at age 9½, he entered the Luitpold Gymnasium, a competitive school. He liked some subjects better than others but progressed through school, again earning high marks. By age 11, he was reading college physics books, and at 13 he decided that Kant was his favorite author after reading the “Critique of Pure Reason.” He was clearly brilliant to anybody paying attention.

Did he flunk math? He did fine in math, but he did flunk the entrance exam to the Zurich Polytechnic when he first took it — when he was about 1 1/2 years away from graduating high school, at age 16, and hadn’t had a lot of French, the language in which the exam was given. He did fine on the math section but failed the language, botany and zoology sections, according to history.com. A 1984 New York Times story says that the essay Einstein wrote for this exam was “full of errors” but pointed to his later interests. He wrote: ”I see myself becoming a teacher of these branches of natural science, choosing the theoretical part of these sciences.

Einstein left the Luitpold Gymnasium and entered the Aargau Cantonal School, where he finished high school — despite continuing trouble with French — and was then automatically admitted in 1896 to the Zurich Polytechnic, from where he graduated.

Did he have a learning disability? Einstein is commonly said to have been dyslexic. It is hard to diagnose posthumously, but the evidence strongly suggests that he was not, several biographers have said. It is also commonly said that he had ADHD — because he daydreamed in school when he was young and was famously forgetful — and Asperger’s Syndrome, a disorder on the autism spectrum characterized by problems with social interaction and repetitive patterns of behavior. In 2003, the BBC reportedthat researchers at Cambridge and Oxford universities said they believed that Einstein (and Isaac Newton) displayed signs of Asperger’s as a young child, when he was a loner and repeated sentences.

Whatever he had, it didn’t stop him from becoming arguably the most famous and brilliant scientist in history! (from an article in the Washington Post)

Math to the Max

May11

How safe is the Boeing 737 MAX series? This emotive question requires us to do some mathematics.

In its current implementation the 737 MAX is no safer than first generation jetliners flying in the late 1950s to early 1960s: types that included the Comet, Caravelle, BAC-111, Trident, VC-10, early 707, 720, DC-8 and Convair 880/890. The 737 MAX is about 75 times as dangerous as the previous 737 NG

The root cause is the installation of the huge LEAP engines on a 50 year old airframe has produced an aircraft that is unstable at higher angles of attack. Avionics – notably MCAS – has been included to restore that stability, but has greatly increased the risk of catastrophic loss of flight control in pitch.

Fatal crash rates per million flights

Aircraft and airline safety is often measured in fatal accident rates per million flights (call this FAR). Third and fourth generation aircraft, including the A320, A330, A340, A380, 737–600/700/800/900 and NG, 747–400, 757, 767 and 777 have a FAR of 0.3 or less. The A320 series is 0.11, the 737 Classic and NG series is 0.13 fatal accidents per million flights (Plane crash rates by model). There is some statistical noise, so these small differences are meaningless, as exemplified by Concorde which went from 0 to 11.36 after one accident, but with only 90,000 flights over its long career.

Because of this statistical noise, a single accident in a new aircraft model is concerning, but not very informative. Two early accidents that appear to have the same design related cause – rather than pilot related – become very concerning.

What is the fatal crash rates per million flights of the 737 MAX?

There have been two accidents, but how many flights? Boeing published the number of flights (41,797) after one year of service ending 21 May 2018 and 130 deliveries (see graphic below)

In that 12 months there wee an average of 65 aircraft in service. Simple math suggests 41,797/(12*65) = 53 flights per aircraft per month. Ten months later there are 370 737 MAXs in service. The average of 370 and 130 is 250 and 250*10 = 2500 aircraft months. 2500*53 = 132,500 flights. Added together 41,797 + 132,500 is about 175,000. To be generous lets say 200,000 flights total – it may be higher.

Two fatal accidents in 200,000 flights is 10 fatal crashes per million flights

Both are attributable mainly to design flaws rather than pilot error. Even pilots in Indonesia and Ethiopia flying older 737s have very low accident rates. 10/0.3 is about 30 times acceptable industry standard and 10/0.13 = 75 times the record for the 737–600/700/800/900 and NG series. The FAR of 0.13 is quite a reliable estimate given 18 fatal accidents and 74 million flights.

The 737 MAX – in its current implementation – is a dangerous aircraft.

Fatal accident rates of 10 per million flights have not been seen since the late 1950s early 1960s and only in first generation aircraft like the Comet, Caravelle, BAC-111, Trident, VC-10, early 707, 720, DC-8 and Convair 880/890. The detailed causes of the crashes will no doubt be a complex interaction of flight regimes, avionics (including MCAS), possible hardware failures, and pilot actions. The LEAP engines have made the 737 MAX unstable at high AOA and been accompanied by avionics changes to correct this. But it is clear that more skilled pilots are required to safely fly the 737 MAX than the 737 NG, and that returns the aircraft to the safety level of first generation airliners of the late 50s early 60s. Read more here.

The Good Chalk Talk on Mathematics

May6

Amazing that having the right chalk can make a mathematician work better and feel happier. After all, when has Mathematics been about ‘feeling’? Actually, it is ALL about feeling – about feeling confident, about feeling like taking risk, about feeling good when solving problems and feeling great at a mathematical revelation while sitting at the back of a boring classroom, Click on this pic to enjoy a peep through the chalk-dust of math blackboards.

Measuring Ocean Waves – Wow!

May4

Waves in the Southern Ocean have already been recorded over 20 metres in height, but new research shows they’re getting higher. A small but significant increase of 1.5 metres per second – 8 per cent – was noted by researchers who analysed approximately 4 billion observations from 31 satellites and 80 ocean buoys worldwide.

Although increases of 5 and 8 per cent might not seem like much, if sustained into the future such changes to our climate will have major impacts,” said Professor Ian Young from the University of Melbourne.

The study – published in Science – analysed data from 33 years and detected an increase in winds in the Antarctic Ocean, which increased by 30 centimetres or 5 per cent. It also found extreme winds are increasing in the Pacific and Atlantic oceans near the equator, and the North Atlantic Ocean by around 0.6 metres per second. Such changes bring a number of threats.

These changes have impacts that are felt all over the world. Storm waves can increase coastal erosion, putting coastal settlements and infrastructure at risk.” Young noted that any changes in the Southern Ocean can have a far reaching effect, as it is the “origin for swell that dominates the wave climate of the South Pacific, South Atlantic and Indian Oceans and determines the stability of beaches for much of the Southern Hemisphere”.

The increased wave height and direction have further potential to increase coastal flooding. Researchers are now looking towards the next 100 years, trying to create a predictive global climate model to help foresee any potential wind and wave changes.

We need a better understanding of how much of this change is due to long-term climate change, and how much is due to multi-decadal fluctuations, or cycles.

H3 Notes: This area of research is a very exciting one for young mathematicians to consider. Click here for more career information.

 

Radical Ratios

May2

Taking a person, when squatting, to be approx. a meter in diameter, we end up with the following ‘radical ratios’:

1. The size of a human cell to that person is the same ratio as a person’s size to Rhode Island
2. The size of a virus to a person is the same ratio as a person is to the earth
3. An atom is to a person as a person is to the earth’s orbit around the sun
4. A proton is to a person as a person is to the distance to Alpha Centauri (the solar system closest to the sun)

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Probability – flip a coin for $1b

April30

Here is another chance to look at probability, and one that you might be allowed to play in class! Flip a coin continuously until a tail appears for the first time. If this doesn’t happen until the 20th (or later) flip, you win $1 billion. If the first tail appears before the 20th flip, you must pay $100. Would you play (or should you even play)? More in Post Support soon. H3 Comment: my wife tried this and got a tail on the first flip, so she is taking me out for morning tea!
Here is the online random coin flipper

Guilty or innocent? Math in the Courtroom Part II

April29

In 2003, a Dutch nurse named Lucia de Berk was accused of murdering several patients. She was sent to prison for six years in before her conviction was overturned in 2010. The reason for the overturning? The prosecutor and the judges behind the conviction could not do math correctly.

The grade 11 class delved deep into the mathematics given by the prosecution in de Berk’s case and discussed the reasons why it was flawed. The students understood loud and clear that there are some serious implications of not knowing math.

In the hospital where de Berk worked, many patient deaths happened while de Berk was nursing them. The prosecution argued that the chances of de Berk being innocent while all these deaths occurred was incredibly small. However, this probability is not at all the same as the probability of de Berk being innocent, given the evidence.

DNA Match

Let’s look at an example. Suppose that police pick up a suspect and match her DNA to evidence collected at a crime scene. Suppose that the likelihood of a match, purely by chance, is only 1 in 10,000. So, 9,999 times out of 10,000, the DNA match gets it right – isn’t this also the chance of the suspect being guilty? Not at all. Suppose the city in which the person lives has 500,000 adult inhabitants who could have, theoretically, committed the crime. Given the likelihood of a random DNA match, there is about 50 people in the city would seem to have DNA that also matches the sample. So the chance of the suspect being guilty is only 1 out of 50 – this means ‘almost certainly innocent’, quite contrary to the wrong estimate of ‘almost certainly guilty’!

This is more or less what happened with the case of de Berk. It just so happens that patients die – all too frequently, unfortunately – and we shouldn’t be surprised that there are a lot of unlucky nurses who might falsely be blamed for murderer.” (Source: https://www.isutrecht.nl/2017/02/guilty-innocent-math-goes-wrong-courtroom/)

By Mikko Peltonen, DP Mathematical Studies

Probability to the Defense

April28

So, an appeal was made to the Supreme Court, when it was overturned on the basis of probability arguments. The defense attorney argued that 1/12,000,000 was not the relevant probability (see previous post). In a city the size of Los Angeles, with maybe 2,000,000 couples, the probability was not that small, he argued, that there existed  more than one couple with the required list of characteristics, given that there was one such couple – the convicted pair. On the basis of the binomial probability distribution, and the 1/12,000,000 figure, this probability can be determined to be about 8% – small, but certainly allowing room for reasonable doubt. The court agreed and reversed the earlier guilty verdict!

Probabilities and Courtroom Drama

April26

In 1964 a Los Angeles blond woman with a ponytail snatched a purse from another woman. The thief was spotted entering a yellow car driven by a black man with a beard and a mustache. The police eventually found a blond woman with a ponytail who regularly associated with a bearded and mustachioed black man who owned a yellow car, but there was no hard evidence linking them to the crime. In court, the prosecutor argued that the probability was so low that such a couple existed that the police must have found the actual culprits. The prosecutor assigned the following probabilities to the characteristics in question:

yellow car: 1 in 10 or 1/10
man with a mustache: 1/4
woman with ponytail: 1/10
woman with blond hair: 1/3
black man with beard: 1/10
interracial couple in a car: 1/1000

The prosecutor argued that the characteristics were independent, so the probability that a randomly selected couple would have them all would be:

(1 x 10) x (1 x 4) x (1 x 10) x (1 x 3) x (1 x 10) x (1 x 1000) = 1 in 12,000,000

This, he argued, was a probability so low that the couple must be guilty. The jury agreed and convicted them.” (extract from: Innumeracy-Mathematical Illiteracy and its Consequences)
BUT, the case was appealed to the California Supreme Court. What do you think the outcome was? (more in another post soon)

Mathematics rates 2nd in ‘Best Jobs of 2018’

April24

Careers in STEM — like Mathematician, Statistician, Data Scientist and Actuary — shape the Best Jobs of 2018, which is no deviation from recent trends. However, a job tracked by the Jobs Rated Report for the first time, Genetic Counselor, is No. 1. And with 29% growth outlook, this healthcare field speaks to the advancements rapidly taking over our job landscape. Jobs in Math came out as #2.
In the same vein, the worst job of 2018, Taxi Driver, has seen a sharp decline in hiring outlook with stagnating pay as a result of ride-sharing apps — apps that were scarcely used just five years ago. There’s no telling how much the job landscape will change in another five years ago. Industries, technology and society might change, but the Jobs Rated report has remained consistent in the criteria it uses to rank 220 professions. The following is the complete Jobs Rated report for 2018.

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“Flip for $1 billion”: There’s one chance in 524,288 (2 to the power of 19) that you will wiin and 524,287 divided by 524,288 that you will lose $100. Even though the chance of losing is so high (“almost certain” in statistical language), when youo do win your winnings will more than make up for your losses. In fact, the average payout when playing this game is about $1800 per bet. “Flipping heck!”

George Nobl Problem:

Professor Nobl explained that the correct answer is one hour and 12 minutes. Here is how he solved it, he said. Fred paints a third of a room in one hour, and Mary a half. So together they can paint five-sixths of a room in an hour. To paint the entire room, they will need six-fifths of an hour, or an hour and 12 minutes.

Missing Numbers: ‘five-star’; ‘85000sq m floor area, $703m project with 1327 new underground carparks’; ‘33000 new international visitors,’ $90 million of ….. and 800 jobs. The 300-room, 5-star hotel will … further 150 jobs’; 3000 people or 4000 people for one-off events’.

Number of spare car-parking spaces. How about 8, or 9 with a tiny part of one on the lower right.

What is x? Try substituting 1,2,3,4. I think you have it solved now!

—–

The pink triangle is one third of the area of the square. Use half base x height formula for area of the triangle, etc.

The coffee cup logic puzzle – Answer is Cup 5 as all the others have blocked pipes. 🙂

 

6×6 for the maximum dog pen area of 36 sq meters.

 

Oxford Exam Answer: According to Rebecca Cotton-Barratt, of Christ Church, this maths question tests abstract thinking”

“I’d initially ask the candidate what shape they think will be formed, and then ask them how they can test this hypothesis,” Cotton-Barratt says.

“They might initially try sketching the ladder at different stages – but ultimately what we want is something that we can generalise and that is accurate (you can’t be sure that your drawing is that accurate, particularly when you’re making a sketch on a whiteboard and don’t have a ruler). So eventually they will fall back on maths, and try to model the situation using equations.

“If they get stuck we would ask them what shape the ladder makes with the wall and floor, and they’ll eventually spot that at each stage the ladder is forming a right-angled triangle. Some might then immediately leap to Pythagoras’ Theorem and use that to find the answer (which is that it forms a quarter circle centred on the point where the floor meets the wall).Of course, Pythagoras could easily find the hypotenuse – it is the green line along the water! (Hint: the hypotenuse is always opposite the right angle!)
………………

Frustratingly there is no definitive answer to the riddle, leaving guessers with no choice but to continue scratching their heads.

Dr Kevin Bowman, course leader for Mathematics at the University of Central Lancashire said: ‘You can interpret it in many ways; one way is no more correct than another.

“There’s no ambiguity in the first equation; 3 apples is 30, so one apple is worth 10.
The Fruit Puzzle…
This isn’t the first mind-bending puzzle to sweep the internet in recent months. Earlier this year, National Geographic’s puzzle asking you to identify which direction a bus is travelling in left thousands of adults scratching their heads (see earlier post). One person suggests that, “because all the bananas aren’t the same, you could say that they all represent different amounts. You might even say that the two coconut pieces in the third equation are different sizes, and therefore add up to three quarters or even seven eighths when put together. In that sense, there are an infinite amount of possible answers.”

Dr Kevin Bowman, course leader for Mathematics at the University of Central Lancashire said: ‘You can interpret it in many ways; one way is no more correct than another.

“There’s no ambiguity in the first equation; 3 apples is 30, so one apple is worth 10.”

Another said, “1 apple equals 10, coconut equals 6 and banana bunch equals 4 so your answer is 20.”

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All exterior angles of one coin add up to 360 degrees. Since a coin has 12 sides, each exterior angle = 30 degrees. Two angles are formed between the two coins. Therefore, the angle formed is 60 degrees.

Quite an easy pattern in the Oct 10-11 Post. Subtract the first two numbers to get the first number in the right column; add the first two numbers in the left column to get the last two of the right column!

Parking Lot Puzzle: Turn your computer screen upside down (or stand on your head), then it becomes easy 🙂

In each row, adding gives the last 2 digits and subtracting gives the first.

The blue cherry picker has an extension arm that can’t be seen very well. This has placed the workers closer to the camera and created a strong false sense of scale simply because your eye assumes that the workers should be on the same plane as the base of the cherry picker!

Yes, it was Major General Stanley in the “Pirates of Penzance!” Check out the link in the picture.

The extra rope needed is exactly 2 x pi or 6.28m!

Christmas Teaser: Today is the 1st of January. Bill’s 8th birthday was yesterday, so the day before (December 30) he was still 7 years old. This December he will turn 9 and, next year, will be 10!

What did the math mother feed her new baby? Formula Milk!

What is a bubble? It is a thin sphere of liquid enclosing air (in most cases) or another gas.

Number of toes = 5170

How many Mathematicians to change a light bulb? Why, n+1 of course (one to hold the light)!

Jan 24, 2014: Assuming a free fall rate of 9.8m/sec/sec it would take just 4.06sec to fall 81m.

= 1 (see first line in the post)

Yes, the TV show with hints of Mathematics and Physics (along with the usual tensions of flatmates?) – did you choose 79?

Leonhard Euler (1707-1783) was an incredibly productive mathematician who published almost 900 books! He took an interest in Latin Squares – grids where each row and column each contains a member of a set of numbers. This forms the basis for Sudoku!

Trig Ratios post: yes, the Sine and Cosine ratios are the same when their angles add up to 90 degrees! This relationship can be expressed as: Sine A = Cosine (90-A) or Cosine A = Sine (90-A)
Good work in identifying this trig pattern. Now, here is a follow up questions which we will address in the next post. Does this pattern suggest that there is a link between Sine and Cosine ratios? Come on, come on… be quick with your answer…Yes, well done – of course there must be!!

Yes, zero is an Integer (which keeps to negative and positive integers apart).

Sam had to position himself to make sure that he 8 the chocolate!

There are 7 days in a week (i.e. Modulo 7). 490 days will be the same day that you chose, so the 491st day will be tomorrow!

Yes, C is the missing section – giving the same difference between numbers in the rows and columns.

Other answers:
That’s a mean looking crocodile! Unless, of course, you knew that it measured just 40cm – yes, just over a foot long!! The camera’s wide angle lens has distorted the image and this makes tiny croc look menacing!

Yes, the 100m time for Bolt works out to be 37kms/hr or 22mls/hr. Of course that is just the average time, not the max speed he reached!

Category 3 climbs last approximately 5 kilometres (3.1 miles), have an average grade of 5 percent, and ascend 150 metres (500 feet).

Category 2 climbs are the same length or longer at an 8 percent grade and ascend 500 metres (1,600 feet).

Category 1 climbs last 20 kilometres (12.4 miles) with an average 6 percent grade and ascend 1,500 metres (4,900 feet).

Category H climbs are the hardest including an altitude difference of at least 1,000 metres (3,280 feet) from start to finish and have an average grade of at least 7 percent.
….
Finding missing numbers is great fun and many readers are regular users of Sudoku. In the recent post (July 13) we find that the sum of the numbers in each row and column is 6, 12, ? Therefore, we need to get 18 as the sum in the final row and column. So, 9 is the missing number in order to complete the puzzle.

Great to see some recent posts on Calculus and we hope that some of our junior students (Years 6+) have a close look at these and develop an interest in this (more advanced) Mathematics.

Trend lines are a practical way to analyse the patterns of data over time and are particularly helpful in population, commerce and environmental change, such as the arctic ice post. The best way to find the answer to the question posed in this post is to click on the original article, copy the graph and paste into (e.g.) Word, using the landscape format. Then, using a ruler, carefully draw the same lines that I have shown in the post. This will help arrive at a more accurate answer. When you have the answer, post a comment to the blog and we can check it out to see if you are right (or close). Good luck Junior Mathematician!

1 year = 31 556 926 seconds

1729 – A rather dull number?
The mathematician G. H. Hardy was visiting the Indian mathematician Ramanujan while he was ill in hospital. Hardy was making small talk and remarked that 1729, the number of the taxi that brought him to the hospital, was a rather dull number. “No Hardy!” repled Ramanujan, “It is a very interesting number. It is the smallest number which can be expressed as the sum of two cubes in two different ways!” You see, even “dull” numbers have special properties!

Blog Diary

Dear Blog Diary,

Our night sky has always fascinated H3, and there have been some recent releases of amazing images from our nearby galaxies. The size and sheer complexity of our solar system is staggering and, mathematically, quite difficult to describe because the numbers are simply so big!

The fireworks background gives readers some idea of how students feel when they suddenly get a mathematical concept and can apply it with success. This is what excites learners to do well in their math studies. This is also what inspires teachers to want to help students have these "aha" moments! As the famous Winston Churchill said, "Never, Never, Never, Never, Never give up on your maths!" (Well, he almost said that).

The "x" factor - it was intriguing to see the TED talk post that explained why we use x to indicate an unknown quantity in Algebra. Hope our readers also enjoyed this view on what we take for granted in our everyday Mathematics.

Lewis and Clark explored routes to the American west...all the way to Oregon City where, today, there is a great museum to herald this famous migration period (see link in the post). So, the header image show canoes heading in which direction? East? How do you know? Should mathematicians expect every picture or drawing to point north? NO, of course not! So, to answer the post question - the canoes could be heading in ANY direction!

I had a discussion with a fellow teacher the other day that was along the lines of how sad it was that students today have lost a sense of fine craftsmanship when it comes to products and services. For example, old cameras were beautifully crafted and lasted, with regular servicing, for up to one or two generations. Today, with our "instant society" we are surrounding with products that have little permanency. The revival of fine architecture in the Art Deco movement is a recent highlighted post. In the same way, important mathematical proofs are timeless and give us all a better sense of something solid and permanent in our fragile world. I do hope that students who engage in Mathematics at any level also share this passion for numbers, patterns and proofs that are fixed and reliable signposts in a sea of turbulent ideas and rapid change.

Thanks to the positive feedback from Warren in Perth who wrote, "Congrats and good luck in your crusade to bring the joy and beauty of maths back to schools." See the Welcome page for the full comment. It is always great to have helpful ideas and feedback from blog readers. Again, thanks so much for taking the time to read H3 Maths.

It was in the news recently that Apple was looking to spend some $97 billion - that's 97,000,000,000. At the rate of $1000 a day, it would take an incredible 265,780 years to spend. That's an insane amount of money and it would be a good exercise to work out how this amount could help fix some of the big issues in the world today, such as the debt crisis in Europe, or Global Warming.

Being able to "roughly" work out an answer in Mathematics is called "Approximation". A good example of using this is in the little test post from the New York Times - looking at the rise in median house prices across a period of time. The answer is lower down in this column... :-)

Above is an algebraic expression with two sets of brackets, -
(x+1)(y-2). The brackets mean "multiply" so each bracket is a factor of an expanded algebraic expression. There are four parts to the bracketed factors, hence the term "quadratic" which comes up often in Year 9 and Year 10 (Freshman and Sophomore) grades. As a growing mathematician you will need to become competent with factorising and expanding algebraic terms.

Great to see so many visitors from 17 different countries - a Prime Number as well! Of course, there are more countries in our Visitor list but they did not show up on the new clustr map.

The blog about maths being all about language is really not entirely true...was just waiting for someone to comment! You see, Mathematics is also very much about shapes, patterns and trends, which were left of the list. In fact, maths is really about everything!! (Answer to median house prices = B)

Welcome to our first visitor from South Africa!

Numbers - they are the DNA of Mathematics and some recent posts will focus on the way that different number groups (called Number Sets) behave - very much like the different groups of people that you mix with (or not) at a party!

Making visual connections is an often forgotten focus in Mathematics yet is integral to most maths testing. I hope you enjoy the challenge of finding the right location for the van on Lombard Street! Your need a sense of orientation and scale but it is really not that difficult.

Welcome to our visitor from San Francisco, just after the San Fran posting! This is a great city, with so much architectural and cultural diversity as well as such a wonderful location.

Patterns - now here's a great subject to get your maths juices boiling! Show me a keen math student and I will guarantee that he or she is into patterns! Of course, the true-blue mathematician is also into random patterns - which we call "chaos" - and that is another great math topic to look at at some other (random) time! Do Zebra stripes count as random patterns? ;-)

The importance of a good breakfast is our focus for the weekmix!

Great to see a recent blog visitor from Gresham, Oregon. Great scenery around the Columbia River Gorge including the second highest waterfall in the USA. Home to some good mathematicians too!

A good friend and wonderful Mathematics teacher (now retired but used to live in Gresham too) send through this kind comment from the USA recently; ".. spent some time on your math blog and was very impressed. I am hoping that students are taking advantage of it. I was particularly impressed with your process of getting students to think mathematically and not just look at math as a hallway that is filled with hurdles called classroom exercises. The most exciting part of math is when you open a side door and explore other rooms that may lead to a maze of interrelated opportunities in math explorations." Many thanks!

A visitor reads our blog from the I-95 (see post). Is this a space-time warp from our Dr Who files or a wonky GPS?

Dear Blog,
Over 100 visitors for January. 100 visitors reminds me of the famous story regarding the great mathematician, Carl Friedrich Gauss. He started primary (elementary) school at age 7 and his genius became apparent when his teacher asked the class to add up (the sum) of all (integer) numbers from 1 through 100. Gauss did this almost instantly by noticing 1+100 = 101; 2+99 = 101, 3 + 98 = 101 for a total of 50 pairs. Therefore the total was 50 x 101 = 5050. He may have reached this mentally by doing 50x100=5000 + 50 = 5050? Whatever method, what a quick mathematical mind at such a young age! Yes, Gauss had a keen interest in how numbers worked and this is a key to doing well in Mathematics.

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