Welcome to H3 Maths

Blog Support for Growing Mathematicians

A Visual History of Mathematics

January22

5 Brilliant Mathematicians who impacted the modern world

January17

“Mathematics – you either love or hate it, right? Those who hate math might still have nightmares of showing up for a high school math test unprepared, even years after graduation. Math is, by nature, an abstract subject, and it can be hard to wrap your head around it if you don’t have a good teacher to guide you. [so, get to like your math teacher, no matter what!]

But even if you don’t count yourself a fan of Mathematics, it’s hard to argue that it hasn’t been a vital factor in our rapid change as a society. We reached the moon (see previous post) because of math. Math allowed us to tease out the secrets of DNA, create and transmit electricity over hundreds of miles to power our homes and offices, and gave rise to computers and all that they do for the world. Click on the following link to discover five of the most brilliant mathematicians whose work continues to help shape our modern world, sometimes hundreds of years after their death.” click on this link

Still Reaching for the Moon at 100 years of age!

January10

Katherine Johnson, the now-retired NASA computer whose work on early human spaceflight milestones was highlighted in the blockbuster movie “Hidden Figures,” will publish an autobiography for young readers in September 2019 called “Reaching for the Moon.”
Now 100 years old, Johnson joined the government agency that later became NASA as a human computer in 1953. Such staffers — typically women and, in an unusual hiring decision for the era, sometimes black — were tasked with solving complex mathematical problems by hand, before mechanical computers were available.”

Read more here

Math attitude predicts math altitude in new study

January5

January Math News: “For the first time, scientists have identified the brain pathway that links a positive attitude toward math to achievement in the subject. In a study of elementary school students, researchers found that having a positive attitude about math was connected to better function of the hippocampus, an important memory center in the brain, during performance of arithmetic problems …

Educators have long observed higher math scores in children who show more interest in math and perceive themselves as being better at it. But it has not been clear if this attitude simply reflects other capacities, such as higher intelligence.

The new study found that, even once IQ and other confounding factors were accounted for, a positive attitude toward math still predicted which students had stronger math performance.

The findings will be published online Jan. 24 in Psychological Science.” Read more here

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The Size of Space is Remarkable!

January3

Ultima Thule is more than a billion miles on the far side of Pluto. This snowman-like space rock is approximately twenty miles long by ten miles wide and seems to spin like a propeller through space. Why? It is two objects fused together in a strange motion.

The object was discovered by the Hubble Space Telescope four years ago and named 2014 MU69. A public campaign hosted by NASA renamed it–“Ultima Thule” is a reference to the most distant place beyond the borders of the known world.

Yesterday, the NASA spacecraft New Horizons conducted a successful flyby of this remote space object. Over the next few days, scientists expect to receive more photographs of the most distant object ever visited by a spacecraft. Because the probe is so far from Earth, scientists say data on Ultima Thule will continue streaming to us until September 2020.

New Horizons measures only 7.2 by 6.9 by 8.9 feet. This tiny space probe is blazing through space in excess of 31,000 miles per hour – that’s faster than my Toyota! The scientific sophistication required to engineer and operate such a device are truly remarkable. The probe flew approximately four billion miles to reach Ultima Thule. However, the Milky Way Galaxy is more than 620,000,000,000,000 miles across. In twelve years of space travel, the probe has crossed 0.000645 percent of our galaxy. And the Milky Way is just one of more than two trillion galaxies in the known universe.

Which gives us just a tiny (really, really tiny) look at how large our universe is! For such huge space-time dimensions we require a new type of Mathematics. Here is one for you to check out.

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Should I learn the formula or the method?

January2

Two students are given a problem in mathematics. One memorizes the formula because that’s easier for the moment. The other learns the principle, even though that’s harder at the time. But when the test comes, one student is working much harder over things the other one understands and enjoys. Guess which one ‘understands and enjoys’? That’s right, the one who took time to learn the method!

Math Wizz used Probability to Beat Lotto

December31

Romanian economist Stefan Mandel was struggling to make ends meet. So he came up with an unlikely solution — winning the lottery. But while most people who dream of scooping the jackpot rely on dumb luck, Mandel had other ideas.

Mandel spent his spare time poring over probability papers penned by mathematician Leonardo Fibonacci — and after years of painstaking research, he devised a “number-picking algorithm” which drew on a method he called “combinatorial condensation”.

Under that method, Mr Mandel boasted he could predict five out of six winning numbers — a feat which reduced the number of possible winning combinations down to thousands instead of millions. Along with a group of friends, he bought huge amounts of tickets using all the possible combinations and ended up taking out the top prize — worth over $A26,000.

After paying expenses, he was left with just $A5400, but it was more than enough to bribe officials and escape Romania’s Communist system, and move to Australia to start a new life with his wife and two kids.

But his lotto racket was just getting started — and unlike notorious US lotto scammer Eddie Tipton, Mr Mandel eventually won the lottery 14 times without breaking a single law. Mr Mandel realised that in some draws, the total cost of buying a ticket to play every possible combination was much lower than the grand jackpot prize. Mr Mandel realised that in some draws, the total cost of buying a ticket to play every possible combination was much lower than the grand jackpot prize. Did he get caught?

Read the full story here.

“It’s all about numbers!”

December28

It was one of those nasty family surprises – a family member having an emergency visit to hospital. As the nurse was making the patient comfortable, she was also busy checking the vital stats and noting them down in her log. Her comment was, “It’s all about numbers and I can’t do my job without them!” Yes, Mathematics has a way of being essential to us in essential situations – as well as ordinary ones too.

Oh, our family member is doing well, thank you. See more info on nursing and statistics here.

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The Math of Christmas

December24

In the Bible there are some 300 prophecies concerning the arrival and life of Jesus Christ, the Messiah. Here are 8 of those 300 prophecies and the mathematical probability that they happened:

(1) The Messiah will be born in Bethlehem. (Micah 5:2; Matthew 2:1; Luke 2:4-6)
(2) The Messiah will be a descendant of Jacob. (Numbers 24:17; Matthew 1:2)
(3) The Messiah will enter Jerusalem as a king riding on a donkey. (Zechariah 9:9; Mark 11:4-11)
(4) The Messiah will be betrayed by a friend. (Psalm 41:9; Luke 22:47,48)
(5) The Messiah’s betrayal money will be used to purchase a potter’s field. (Zechariah 11:13; Matthew 27:9,10)
(6) The Messiah will be spat upon and struck. (Isaiah 50:6; Matthew 26:67)
(7) The Messiah’s hands and feet will be pierced. (Psalm 22:16; John 20:25-27)
(8) Soldiers will gamble for the Messiah’s garments. (Psalm 22:18; Luke 23:34)

There is no way one man could have fulfilled all 8 of these prophecies unless God was making it happen. Who else controls history? Who else could give us such irrefutable proof for Christianity? The odds are one in one hundred quadrillion, or 1 in 100,000,000,000,000,000.

This mathematical proof was calculated by Professor Peter Stoner. He was chairman of the mathematics and astronomy departments at Pasadena City College until 1953. He then went to Westmont College in Santa Barbara, California, where he served as chairman of the science division.

You don’t have to be a mathematics professor to see that this evidence is irrefutable.

source of article in Christian Post here

 

Find x

December17

see Post Support for answer–>

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

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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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