Ancient Grecian Urn

Grecian UrnJust imagine all the engaging math lessons this beautiful Grecian Urn can inspire!

Look at all the patterns on its surface. How many do you count? There are lots of geometric shapes making up the patterns. I see triangles, rhombi, and squares. I also see some funny shapes that have one curved side, like the people kneeling, and some shapes that have lots of sides and go on and on and on all around the urn in the part that looks like a maze. What names would you give these shapes?

Notice the cracks covering the urn’s surface. It is very old, and was buried underground for many years, probably thousands! The archaeologists, people who study human history, who found it had to put it back together, piece by piece, like a big 3D puzzle. Do you think it was tricky? I think the patterns might have given them a few clues!

I don’t think those patterns were easy to carve, though. Back when this urn was decorated, the design had to be carefully thought out, drawn, and measured, all by hand! The Ancient Greeks only had simple tools to help them, not powerful electric tools and computer programs like we have today. Do you think you could plan a design for an urn without any technology? Give it a try!

Where else do you see patterns in the world around you? Dishes are still decorated with patterns that go all the way around! And 9’s favorite sweater has a repeating pattern of black and white stripes, just like the stripes on this urn. What other patterns do you use or see every day?

Greece’s Rio-Antirrio Bridge

rio-antirrio bridge

The proof of arithmetic is everywhere you look.  On my recent trip to Greece, this was proven profoundly through the artifacts and architecture in and around this gorgeous city. One of the most spectacular examples of the vivid world of arithmetic lives within the Rio-Antirrio Bridge, one of the world’s longest suspension bridges.

The support cables create a sail-like appearance!

The bridge is supported by four pylons; these are the large posts that reach from the bottom of the Gulf of Corinth to a whopping max of 524 feet (160m) above sea-level. Reaching further into the architecture arithmetic, each pylon splits into four beams creating an open area square pyramid atop the initial hexagonal structure of the lower pylon. This design was chosen in order to limit the amount of wind contact on each part of the bridge. The base of each pylon sits on the bottom of the gulf and is able to move laterally to absorb potential seismic activity.

Despite the use of the pylons, no part of the actual bridge is supported by the pylons, but by a multitude of suspension cables. Eight sets of 23 suspension cables connect from the top of each pylon to each of the five spans. The spans are all connected by six different expansion joints. When added together, they total an impressive 9,449 feet (2880m) in length across a 2- mile (3 km) expanse of water.

With so many visual measurements, basic arithmetic is easy to accomplish. How many support cables are there? How many pylons can you see? What shape is at the top of each pylon? These are just a few questions you could ask to stir immersive and critical learning centered around travel and bridges.

For more information see the links below.

https://en.wikipedia.org/wiki/Rio%E2%80%93Antirrio_bridge

http://www.industrytap.com/rio-antirrio-bridge-the-worlds-longest-multi-span-cable-system/3756

http://www.drgeorgepc.com/ArtRionAntirionBridge.html

What is Pi?

What is Pi?

Hey there kids, my name is Pi

pi

 

 

 

 

 

 

I’m the irrational, never-ending number guy

You might see me written as 3.14

But, in fact, I’m really so much more

I’m the ratio of a circle’s circumference to diameter

But, please don’t define me just by that parameter

No matter the size of your circled design

I’m always the same number, you’ll find

But what IS that number?

Well, that’s hard to say

Because it goes on forever!

You’d write more every day!

I have so many digits after 3.14

You could write on for years and still get many more

You could write 3.141592653589793238

But, you’d still have more to calculate!

So, think of me more as a circular friend

Whose friendship really has no end.

 

Pi in the Sky

Pi day is coming and I am excited. Math is rarely assigned its own holidays, so the idea of spending an entire 24 hours hailing the art and mystery of pi is certainly cause for celebration.

Yes, on March 14, which is pi rounded to the three first digits – 3.14, millions of little boys and girls will demonstrate their mathematical prowess by loudly proclaiming memorized speeches of pi calculations to the umpteenth digit. As in 3.14159265358979…etc, etc.

But are number recitals the best way to celebrate what pi is all about? Is the discussion of digits doing it justice?

Just what is so great about pi, anyway?

Take a Slice of Pi

Pi is defined as the ratio of a circumference of a circle to its diameter, no matter the circle’s size. It’s an easy concept to comprehend and observe – measurable with a piece of string – but a difficult one to calculate. In fact, it’s a never-ending irrational number – which means its exact value is pretty much unknowable. Although you could spend years of your life continuing to calculate pi to the next digit, you’d expire before discerning a pattern or an end. It goes on forever.

As such, there is a romantic relationship between pi and the infinite, although ancient mathematicians found the concept of irrational numbers an affront to the idea of divine omniscience. How could something be inherently unknowable – even to the almighty?

The Nature of Pi

Pi is logically tied to circles, but also relates to the cycles of nature. Pi appears as part of the Fourier series in mathematics, which represents periodic and wave-like oscillating functions. It’s the foundation of the physics that describes waves and ripples of light and sound.

Pi is also linked to the meandering ratio of a river, or the ratio of a river’s length to its source. Although that number varies depending on the direction and curves of a river, the average meandering ratio comes close to pi.

Pi was an essential element of NASA spacecraft trajectory calculations, as evidenced by the recent movie, “Hidden Figures.” Without it, perhaps John Glenn’s miraculous orbit would have fallen short of its objective.

It can also be found in Heisenberg’s uncertainty principle, which examines the characteristics of sub-atomic particles, thus revealing pi’s importance in understanding the very nature of the universe.

Can you understand why pi is such a fascinating concept and worthy of so much more than digital regurgitation? Let’s think of new ways to celebrate it – what do you think?

Visit the shop to purchase my plush “Pi” figure for children and other pi products!

Watch my videos to learn more about pi!

What Are Roman Numerals?

Hey there kids – it’s number 2!

number2Have I got an interesting topic for you!

You’ve met numbers 1 through 9
Let’s learn about different ones this time!

Roman numerals are good to know
They were used to express value a long time ago

Instead of writing 1,2, 3
Try the Roman way with I, II, III – see?

Roman numerals are used today
On some clocks, in books and plays

But what’s so cool about when you use ‘em
Is how hard it is to really confuse ‘em

Let’s take a Roman numeral tour
And learn to write 1, 2, 3, and 4

I, II, III are easy to see
But, 4 is IV– how can that be?

Because 4 is one less than 5, we show
IV which is “I” less than 5 or “V,” Oh!

Roman numerals use “I” after or before
To show one less or even one more

VI is 6 and VII is 7, then
VIII is8, IX is 9 -one less than “X” (or 10!)

Roman numerals are a great way to learn
A new way of viewing numbers – now it’s your turn!

Talk to your teacher or mom or dad,
About using Roman numerals to subtract or add.

 

1 2 3 4 8