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# June 2018 Editors' Picks

June 8, 2018

Do you enjoy exploring mathematics? We certainly do. In fact, at One on Epsilon we thrive on great Youtube mathematics videos. Our team is made up of mathematicians, teachers, and parents and we love seeking out exceptional Youtube videos that do a great job at presenting and investigating mathematics.

We continuosly work to improve our free educational app Epsilon Stream. It allows users like you to search mathematics terms in the world of K-12 mathematics as well as exploratory mathematics. Key in any search term and see great selected resources, all hand picked and guaranteed to be both precise and engaging.

As we do every month, our Editors' picks presents you with a few selected high quality videos across a range of topics and channels. This month we are also experimenting with suggesting some additional activities and thought points for each video. If you are a formal educator, you may try these with your class. Alternatively, if you are a student or enthusiast, just give your brain a jog and think about these points yourself. Let's get started!

How Eratosthenes calculated the Earth's circumference by Business Insider: This video presents an interesting idea developed by Eratosthenes, an ancient Greek mathematician who estimated the circumference of the earth. Are you curious about how Eratosthenes did this? Pause the video at 1'38'' and see if you can figure out his method with the given information.

Eratosthenes's clever thinking uses Euclidean Geometry, methods from trigonometry, circumference of a circle, and proportions. His approximation turned out to be quite close to modern measurements. It is truly a spark of an idea over 2,000 years ago that came from a brilliant mind.

Did you notice that according to the video, Eratosthenes used the unit of stadia to measure the distance between Alexandria and Syene? Stadia (or Stadium in Latin) was an ancient Greek unit of length. Today, the exact distance of a stadia is not agreed upon. Perhaps this dispute can affect the result of Eratosthenes's calculation. Why don't you check out more yourself?

Arthur Benjamin presents The magic of Fibonacci numbers by TED: So many inspirational people have presented passionate TED talks. This talk doesn't fall short. ‘Mathemagician’ Arthur Benjamin takes us onto a journey that explores hidden properties of the famous Fibonacci sequence. If you are new to the Fibonacci sequence, try this first. The first few terms of the sequence are 1, 2, 3, 5, 8. Take a moment, and try to figure out the next few terms. Can you come up with a pattern for this sequence? If not, don't worry. Let's watch the video. While you are watching the video, we would encourage you to pause the video and follow along with Arthur Benjamin's calculations.

Did you also discover the hidden properties that the presenter, Arthur Benjamin, shared with us? The message that we are taking from Arthur's presentation is to pay more attention to the important aspect of mathematics applications – learning how to think. Do you agree?

Pythagorean Theorem: Six Proofs by Beau Janzen: We have recently shared some beautiful visual representations of the Pythagorean Theorem proof (see the March 2018 Editors' Picks and November 2017 Editors' Picks). Also, if you would like to brush-up on the Pythagorean Theorem, check out this Math is Fun page.

This video combines six proofs in one short presentation! Have a look of this video and tell us which one is your favorite. If you feel it goes a bit fast, try to pause frequently or watch several times to get your head around it.

Can you find a right triangle with integer side lengths? These integers are called Pythagorean Triples. How many sets of Pythagorean triples can you find? How many are there?

Divisibility By 7 Graph Visualization by MindYourDecisions: This video provides us with a neat procedure that checks whether an integer can be divided by 7. Not only that, it also shows the remainder. Follow the video and try your own number.

Have you wondered why this procedure works? For instance, why are the green arrows pointing to the numbers they are pointing to? (1 to 3; 2 to 6; 3 to 2...). Can you come up with a graph to test divisibility by 2? 5? 9? This is quite a challenge.

Angles Song by NUMBEROCK Math Songs:  While there is a danger of being "extra cheesy", a catchy song can still be a great learning strategy while providing some brain breaks. We have one for you about angles to finish off this month's Editors' Picks:

There are so many things you can explore with this song. For example, what are the different types of angles? How do you use a protractor to measure an angle? Where can you find these angles in everyday life? And much more...

We hope you found these videos inspiring. Don’t forget to check out our free Epsilon Stream App for more quality videos. Also, check out our new website for more updates. You may also follow us on Twitter, @OneOnEpsilon for daily updates.

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