New York City,
located in the Northeastern section of the United States may be known for its
rude taxi drivers, towering skyscrapers, and fictional superhero teams, but now
educators everywhere may know it for something else. It’s mathematical
importance.
Located across from
Madison Square Gardens, this two year old toddler of a museum isn’t aimed at
teaching you the boring history of who wrote which equation and why it matters.
It’s just aimed at teaching you how to have fun; by subconsciously teaching you
those boring equations you dreaded that was going to accompany the tour.
It’s not just
another museum in the U.S., it’s the only one if its kind. In an age where
teenagers dropping out of school is commonality and the ability to Google from
home is considered by some a “basic human right”, how is our education so low?
I have some opinions on that but I think it best to keep those to myself for
now…
Let’s take an
unguided tour of this interesting, one-of-a-kind museum and maybe learn
something along the way. We’ll also explore a few other math museums around the
world, talk about an eccentric named Pythagoras, and explain how a shuttle can
roll over acorn shaped balls without bouncing like a washing machine with a
boot in it.
Let’s start by going
back to school first.
‘Merica. It Ranks
“21th”
NBC popularized the
phrase “The More You Know” with its educational sound bites featuring popular
celebrities doling out 30 seconds of random trivia. It was nice and all while
it lasted, you learned some cool things to help you out in your next round of
Apples to Apples, but then they turn around and run a graphic like the one
pictured above, all the while slamming modern educators for their inability to
teach during the segment…kudos NBC, sounds like you should stop blaming your
professor, put down the bongs, and go back to class.
Aside from the
obvious and glaring typo featured prominently in a different color font in the
middle, this graphic is right. This is what America currently ranks in these
three categories and as time goes on, it’s only going to decline further.
Semi-developed nations have higher graduation rates then we do. And in some of
those countries education is frowned
upon. Just let that sink in for a moment.
The most appalling
thing about this (to me anyway) is these statistics are coming in during a day
and age where education should be the easiest to obtain. MIT offers free
coursework online for you take virtually any
of their hundreds of classes from home FOR FREE! Google and Wikipedia while not
always 100% accurate are excellent resources when searching for knowledge (how
do you think I research 90% of these articles?)
The government does
nothing to help in this fact. They drown the average college student in so much
debt they don’t start bringing in an income usually until their 4th-5th
year after graduation, all of it goes to paying off loans. No wonder so many
American kids don’t want to go to college. Who wants to sell their kidney and
half a liver just to get a lecture on Quantum Theory?
17th in
problem solving…
That means beating
things till they work is how we most commonly attain a solution to complex
problems…
So what can we do?
Well for starters we can stop attacking the educators when our students are
failing classes and start working with the students. The comic strip below
couldn’t illustrate this fact any better.
Programs like
General Mills’ box tops for education and local fundraisers are good starts,
but the best idea (once again in my opinion) so far has to go to the MoMath
Museum. Part of the problem with education then and now is that it isn’t fun,
some educators just aren’t engaging enough, especially for this highspeed
flashy picture generation.
So just exactly how
does this awesome institute make learning so much fun?
The
MoMath Museum of Mathematics (and FUN!)
As you can tell
from that classy gentleman’s example above that not only can riding on a
tricycle made of mathematical theory be fun for all ages, it gets you asking a
lot of questions. First and foremost, where can I get one of those? Secondly
(and most importantly) if square wheels aren’t supposed to roll how is he
riding that? And thirdly, wouldn’t that be bumpy as all heck?
Well I’ll answer
all those questions right now. First, you can build one. In fact you can make
your wheels any shape you want. Fancy a triangle? You can build a road for that.
A crescent moon, a pentagon, the silhouette of a chicken???
Well, while they’re
all possible a chicken silhouette might be harder then you want to deal with.
But any two dimensional, geometric shape you can dream up, you can build a
wheel and road for. There are just a few things you have to keep in mind.
When you make your
bike all three wheels have to be different sizes if you want to build a circle
track like the one at the museum. The reason? As your individual sections
coalesce and eventually meet in the middle the spacing between the sections width
change. This interferes with the most important part of the whole shebang. The
axle. As long as you keep the axle traveling at the same distance from the
ground at all times you’ll roll along smoothly.
The one at MoMath
Museum operates on the principle of Catenary Curves. Chances are there’s a
catenary curve not far from you right now. The power lines, bridges, cords, and
chains, all operate on this mathematical principle. Catenary curves are just
the natural drop a length of chain, cord, or rope that bows under the natural
weight of itself when suspended only by the two ends. Here, it may be easier to
just show you.
See how the mid-section of the chain drops
when hung from two nails on either side? The furthest downward point of this is
the catenary curve of the chain. Catenary curves can be inverse as well, such
as the geometric shaping of the circular path at MoMath…
That’s the Sheffield Winter Gardens in
Europe. It’s the largest of its kind in the United Kingdom, and the greenest of
its kind in the world. Seriously. The inverted catenary curves that make up the
buildings arched structure are made from the tree, The Larch. The Larch comes
from sustainable forests and doesn’t need any kind of stain or solvents in
order to protect. Because of this the plants are exposed to even less chemicals
then they would be anywhere else. Clever, clever Europe. I knew I loved you guys.
The next one we’re going to talk about is a
bizarre pulley style ride for kids and adults alike that might just change your
mind on how geometric shapes work. Turns out, you don’t need a spherical shape
like a ball to roll across.
While that glass raft in that enclosure may
look like its rolling over balls its actually not. It’s rolling over what is
commonly known as the Reuleaux Triangle, well…maybe not as commonly as I thought;
perhaps an acorn shape better suits it. But where a natural acorn shape has
some deformities most times that interrupt a uniform size and shape, these are
manufactured with precision to provide a smooth ride.
Turns out this isn’t anything new (well, the
ride is, but the concept on the other hand…). In 1860 a guy named Joseph-Émile
Barbier, building upon known principles of geometry, devised a theorem. It
states that every curve of a constant width has a perimeter of pi multiplied by
the objects width. Years later, a German mathematician named Franz Reuleaux
would build even further upon these by creating the polygons his predecessor
had most likely envisioned.
The geometric shape in the upper left hand
corner is the Reuleaux Triangle. This is the object found supporting the raft.
Because it has equal width, shape, and height when moved to any of its three
sides this shape creates a uniform surface for the raft to roll across in the
pit no matter which direction any of the hundred or so of them may be turned.
It’s quite remarkable when you think about it.
Still having trouble understanding how a
Reuleaux Triangle works? A blogger by the pen name of Pwsiegel has written a
thoughtful blog detailing exactly how you can create your own Reuleaux polygons
to get a better handling on this geometrical wonder. You can find it by clicking
here.
With 38 other exhibits and many more to come
this museum is truly astonishing for children and adults alike. It distills the
fear of math by un-complicating the complicated with simple examples displaying
how math is truly used around us on a large and very recognizable scale. If you
ever get the chance take a trip to the museum for yourself.
Or maybe you’re more into the hardcore algorithms
and complex calculus equations. Well if that’s your speed smarty guy then maybe
you should check out some of these other awesome mathematical museums from
around the world.
Mathematikum, Giessen, Germany
Much like MoMath in New York City, Mathematikum
in Germany has a very hands-on approach to teaching kids math. With 150
exhibits, 150,000 tourists annually, the fact that it’s open all week, and the
interactive mathematician Tuesdays where a professor comes in to speak to the
public and be interviewed, this is truly a place to visit for the math
enthusiast.
The Garden of Archimedes, Florence, Italy
This gorgeous museum in Italy has three
permanent galleries. One is dedicated to curves. That’s right, geometry baby,
sexy, sexy, curvy, geometry. Okay…so maybe it isn’t sexy, but it is
informative. The next gallery is dedicated to the history of mathematics going
all the way back to their discovery in the Islamic world from the Renaissance,
and all the way up to modern times. The final gallery, and the final segment
we’ll talk briefly about today, is dedicated to the man known as both
Pythagoras and Pitigora. That’s right, a math genius so brilliant he gets his
own gallery, and two spellings for his name.
Palais de la Découverte (Palace of
Discovery) Paris,
France
This museum located in the Grand Palace
section of Paris, France is no exception to the others on this list. Like
Mathematikum and Garden of Archimedes it offers hands-on experience. With
workshops ranging from Astrophysics to Earth Sciences, they aim to improve your
knowledge in almost any field of science you can imagine. It also offers
mathematics workshops as well, hence how it made it onto this list (and it’s an
awesome museum! Check it out!)
Techniquest, Cardiff, Wales
Even though it was established in 1986 it
wasn’t until almost ten years later that Techniquest in Cardiff, Wales found
itself a permanent home. The final one we’ll be discussing on this list today
is another located across the pond that also offers a wide array of hands-on
experiments to make you feel like a mad scientist. For the mathematically
inquisitive it offers a vast amount of exhibits and puzzles to satiate your
brainiac desires.
And now, as promised, a man with his own
theory, biographies written hundreds of years after his death, and his very own
religion that is now somewhat re-emerging in modern times (oh yay, another
flying spaghetti monster…), Pythagoras the eccentric.
Pythagoras’ Theorem,
Thoughts, and Theology
Pythagoras of Samos
was an interesting fellow. Forget the Dos Equis guy, the mystery surrounding
Pythagoras and his bizarre life were written down posthumously. And not just a
few weeks after he died, we’re talking centuries. You can imagine if a story can
change from one end of the lunch table to the other, imagine how the story of a
man like Pythagoras can shift over time.
There is one huge
remnant of Pythagoras however left behind, and that is his contribution to
mathematics. Pythagoras is often credited with the, as you can assume,
Pythagorean Theorem. This theory states that the square of the hypotenuse (the
side opposite the right angle) is equal to the sum of the squares of the other
two sides. The theorem can be written as an equation relating the lengths of
the sides a, b and c, often called the Pythagorean equation.
To put it more
simply. When a triangle has a 90 degree angle and squares are drawn on all
three sides the two smaller squares, when added together, will have the same
area as the bigger one. Take a look at the picture below.
There is evidence
that the ancient Mesopotamians may have discovered this first around 1800 B.C.,
and the Egyptians and Chinese had made similar discoveries as well, Pythagoras
was the first one to develop a mathematical example of this principle. For this
reason he is credited with the name of the theorem, but that wouldn’t be the
last of this Greek nomad’s contribution to history.
According to lore,
Pythagoras’ beliefs in the supernatural, spiritual, and scientific were not
mutually exclusive to one another. In fact he embraced them all into one
amalgamation so unique that it would become topic of conversation for great
philosophers such as Aristotle and even Plato. He didn’t just develop a Theorem
for mathematics, somehow, along the line; he developed himself into a
divination.
He believed in
multiple reincarnations and was a staunch believer he had already been through
the process four times. In one of his past lives he was a beautiful courtesan
(remember prostitution used to be respectable) and he could recall each life in
vivid detail. He believed by the time you got to the end of the line you would
become immortal. I haven’t met anyone yet who has fulfilled Pythagoreanism’s
lofty prophecy, but I’ll keep my fingers crossed.
In 530 B.C.,
Pythagoras moved to Croton in then Magna Graecia and set up shop for his
religious gobble-dee-gook. Peddling transmigration of the soul and attunement
to the cosmos through mathematics during a time where none of this was understood
wasn’t exactly a hard task. (In fact, modern pharmaceutical corporations I
think still follow this business model.) And it spread like wild fire.
Speaking of fire,
the government didn’t like the conflicting views to religion this brought about
in an already heavily oppressed society. Temples of worship for Pythagoreans
were burned, followers were put to death, and inevitably Pythagoras had to flee
the city.
But not before
paving the way for Platoism and paving the way for modern mathematics, and for that
Pythagoras of Samos, I salute you. Hope you enjoyed reading this today! Feel
free to share it around on Facebook!
-Ryan Sanders
To
learn more about Pythagoras, MoMath in New York, or plan a trip to a math
museum somewhere else here in America, feel free to visit any of the links
posted below. Thanks for reading! And as always SOCIAL MEDIA THIS AROUND!!! :D
Thanks for reading. Happy Learning!
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