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Blog Support for Growing Mathematicians

The Astonishing Greek Calculating Machine

September19

A hundred and twenty years ago, divers discovered a shipwreck off the island of Antikythera in Greece. What they found changed our understanding of human history. It was the oldest example of an analogue computer used to predict astronomical positions and eclipses decades in advance. Simply incredible!

The mysterious Antikythera Mechanism has captured the imagination of archaeologists, mathematicians, and scientists ever since. Now, using the latest 3D x-ray and modelling technology, experts are unravelling the secrets of what this machine may have been capable of. See the video here:

https://www.bbc.com/reel/video/p09pcwnz/unlocking-the-secrets-of-the-world-s-oldest-computer

iPhone 13 has power in spades

September15

“The iPhone 13 is powered by a new chip designed by Apple: the A15 Bionic. Executives called the chip the “fastest CPU in any smartphone.” It uses 5-nanometer technology and includes 15 billion transistors, a 6-core CPU and 4-core GPU. The technology will give the iPhone improved machine learning capabilities, such as real-time video analysis and the ability to analyze text in photos.”

Yes, you read that right, 15 billion transistors! That over double what mobile phones had just three years ago, and all crammed into a tiny space. Which begs the question, how do you get that many transistors together? And, why are so many needed? Here’s why:

Let us say a transistor can store a bit. When it is ON it is ‘1’ and when it is OFF it is ‘0’.
Now to store a byte (8 bits) we need 8 transistors.
to store 1 kB 8*1024
to store 1 MB 8*1048576 transistor
to store 1GB i.e. a billion bytes we need 8 billion transistors.

We have so far considered only memory. Now add the processor, graphic unit, network and other interface etc etc. Hope you get it. [source: quota]

 

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Turn one sphere into two identical copies, simply by rearranging its pieces

August31

https://www.quantamagazine.org/how-a-mathematical-paradox-allows-infinite-cloning-20210826/

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No, not another cartoon…

August24

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The Collatz Conjecture – simple math problem no one can solve!

August8

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Fun with Grapher

July31

If you are on an Apple device, look for the app called Grapher under the Applications–>Utilities folder. Choose 3D and type in anything that you think will make an interesting graph. You can use the ^ key to make powers. You can also animate your graph to see its shape change. Very cool and very mathematical! And, of course, a nice follow on post from the last one.
Follow up questions: Will this shape be stronger than a regular corrugated one? Could you make different shapes to test for the best one to take a load (the old ‘Bridge-Building’ challenge). Do you have access to a cnc lathe to make your favorite shape?

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Looking at buildings can produce headaches. Math explains why.

July31

“It’s three o’clock. You’re at work, struggling to focus during the afternoon lull. You gaze out of your office window, hoping for some relief, but instead you feel a headache coming on. Flat gray concrete lines the streets, while windows form repetitive glassy intervals in stark brick walls. With monotonous straight lines as far as the eye can see, there’s nowhere pleasant to rest your gaze.” Try to focus on this picture of the building while scrolling your screen up and down! Here is another example:
Mathematician Jean-Baptiste Joseph Fourier (left) showed that we can think of scenes as being made up of striped patterns, of different sizes, orientations and positions, all added together. These patterns are called Fourier Components. In mathematics, a Fourier series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. You can create these on your calculator or computer:

Urban scenes break the rule of nature: they tend to feature regular, repetitive patterns, due to the common use of design features such as windows, staircases and railings.

Regular patterns of this kind are rarely found in nature. Because the repetitive patterns of urban architecture break the rule of nature, it is more difficult for the human brain to process them efficiently. And because urban landscapes are not as easy to process, they are less comfortable to look at. Some patterns, such as the stripes on door mats, carpets and escalator stair treads can trigger headaches and even epileptic seizures.

A way to measure the efficiency of the brain’s visual processes is to measure the amount of oxygen used by the visual part of the brain, located at the back of the head. When the brain uses oxygen, it changes color. We can track these changes by shining infrared light onto the scalp, and measuring the scattered light which bounces back off the brain and through the skull. Typically, oxygen usage is greater when people look at uncomfortable images, such as urban scenes.” [Read the entire article here] Finally, how would you like living in this room?

This room was created by Peter Kogler, an internationally renowned Austrian artist who creates hypnotic installations. They’ll make you dizzy just by looking at them on the internet, but imagine actually being in one. (Major #vertigo risk here, guys.) Kohler lives and works in Vienna and recently had a psychedelic installation at the ING Art Center in Brussels. Using paint and projections, he turns ordinary galleries, lobbies and transit centers into distorted, curving, twisted experiences. Perhaps, after all, that is what Mathematics is all about—one distorted, twisted experience? LOL!

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Another Great Book for Math Teachers

July23

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Jeff Bezos and passengers lift off into space with no pilot!

July22

Jeff Bezos and his fellow passengers rocketed into space, coinciding with the day in 1969 when Neil Armstrong became the first man to walk on the moon. What an achievement!

Get this—a current iPhone seven million times more memory than the guidance computer on Armstrong’s spaceship and over one hundred thousand times its processing power.

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Free PPT on History and Exploring Pi

July10

Pi is one of the main attractions inside the Secret Garden of Mathematics. Pi is delightful, mysterious, simple, yet profound. Pi contains the name of the person you will marry, where you will live and, perhaps, your favourite song. Share this free ppt with your teacher or with your class. Change it to fit the group you are sharing it with or, best of all, share it with some free pie! Origin and History of Pi

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Post Support

Algebra Puzzle: Answer = 1

Popular Math Problems Answers: 1, 1

Number of tabs? According to Lifehacker, the ideal number of tabs you should have open is nine. Yes, a single digit. To some, this is like playing a piano and only using a fraction of the notes!

Worst Graph? Where to start. What a visual mess and even some of the lines merge and are impossible to follow. A graph is a visual display of data, with the goal to identify trends or patterns. This is a spider’s web of information which fails to show a clear pattern at all. Solution? Well, different colors would help, or why not group in two or three graphs where trends are similar?

Number of different nets to make a cube is eleven – see this link

Homework Puzzle; The total value of the counters is 486, so halve this to get 243. Now, arrange the counters to equal this amount twice.

The graph on the left (Coronavirus) is for a time period of 30 days, while the one on the right (SARS) is for 8 months! Very poor graphical comparison and hardly relevant, unless it is attempting to downplay the seriousness of the coronavirus?

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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