Geometry: The Voluminous “Vessel” at Hudson Yards

Calling all NYC dwellers! Have you seen the new structure at Hudson Yards?  A staircase to nowhere, this bee-hive like structure is for the true adventurists at heart; Clearly, I had to check it out!

Where does math come in here you say?  Well, during my exploration, I had to wonder (as am sure most people do) what is the volume of this structure?  What do you think the volume of the Vessel is? (Hint: feel free to approximate!)

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Solution: I estimated the volume by using the formula of a three-dimensional cone. (Not an exact measurement of the Vessel, but close enough!) .

Screen Shot 2019-04-11 at 5.08.42 PM Screen Shot 2019-04-12 at 1.20.08 PM.pngWe can find the radius and height based on the given information above.  Everything we need for our formula is right here!

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Now that we have our information, let’s fill in our formula and calculate! Screen Shot 2019-04-11 at 5.14.58 PM.pngScreen Shot 2019-04-11 at 5.17.30 PM.png

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Extra Tip! Notice that we labeled the solution with feet cubed Screen Shot 2019-04-14 at 4.53.49 PM.png, which is the short-handed way to write “feet cubed.”  Why feet cubed instead of feet squared? Or just plain old feet? When we use our formula we are multiplying three numbers all measured in feet:

radius X radius X (Height/3)

All three values are measured in feet! –> Feet cubed (Screen Shot 2019-04-14 at 4.53.49 PM.png)

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Did you get the same answer? Did you use a different method or have any questions?  Let me know in the comments and happy mathing! 🙂

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Algebra: Rate of Change

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Extra Tip! Notice that we added the labels feet/second to our answer.  Why does this make sense?? The question tells us that P(t) represents feet and that t is equal to seconds.  Another way to look at this question when applying it to the slope formula is to realize that we are finding the change of feet divided by the change of seconds.                                                          ____________________________________________________________________________________

Still got questions?  Let me know in the comments and as always happy calculating!:)

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Geometry: Intersecting Secants

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*Extra Tip! Why does this formula work in the first place!??  If we draw lines creating and proving triangle RTQ and triangle RPS are similar by AA, this leads us to know that the two triangles have proportionate sides and can follow our formula!         ___________________________________________________________________________________

Still got questions?  Let me know in the comments and remeber having questions is a  good thing!

Also, happy holidays from Mathsux! May your December break be filled with family, food, happiness, and maybe some math problems! 🙂

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The Magic of the “Golden Ratio”

Walking around NYC, I was on a mission to connect mathematics to the real world.  This, of course, led me to go on a mathematical scavenger hunt in search of  the “Golden Ratio.” Hidden in plain sight, this often times naturally occurring ratio is seen everywhere from historic and modern architecture to nature itself. 

What is this all-encompassing “Golden Ratio” you may ask?
It’s a proportion, related to a never-ending sequence of numbers called the Fibonacci sequence, and is considered to be the most pleasing ratio to the human eye.  The ratio itself is an irrational number equal to 1.618……..(etc.).

Why should you care?
When the same ratio is seen in the Parthenon, the Taj Mahal, the Mona Lisa and on the shores of a beach in a seashell, you know it must be something special!
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Random as it may seem, this proportion stems from the following sequence of numbers, known as the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, 21, …….

Do you notice what pattern these numbers form?
Capture(Answer: Each previous two numbers are added together to find the next number.)

The Golden RectangleThe most common example of the “Golden Ratio” can be seen in the Golden rectangle.  The lengths of this rectangle are in the proportion from 1: 1.618 following the golden ratio. Behold the beauty of the Golden Rectangle:

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How is the Fibonacci Sequence related to the Golden Ratio?                                               What if we drew a golden rectangle within our rectangle?

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Then drew another golden rectangle within that golden rectangle?

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And we kept doing this until we could no longer see what we were doing…….

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The proportion between the width and height of these rectangles is 1.618 and can also be shown as the proportion between any two numbers in the Fibonacci sequence as the sequence approaches infinity. Notice that the area of each rectangle in the Fibonacci sequence is represented below in increasing size:Screen Shot 2018-11-19 at 10.31.51 PM

Where exactly can you find this Golden Ratio in real life? Found in NYC! The Golden ratio was seen here at the United Nations Secretariat building in the form of a golden rectangle(s).  Check it out!

Golden Ratio Pic

Where have you seen this proportion of magical magnitude?  Look for it in your own city or town and let me know what you find! Happy Golden Ratio hunting! 🙂

If you’re interested in learning more about the golden ratio and are also a big Disney fan, I highly recommend you check out Donald Duck’s Math Magic!

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Summertime Review: Factoring

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Whether you are ready to go back to school or back to sleep, I hope you found this factoring review helpful.

Still got questions?  Don’t hesitate to reach out in the comments below! Happy math-ing! 🙂

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‘Math Suks’ ~ Jimmy Buffett

Need to relax after studying? Close to wanting to “burn your textbook”? This super chill and somewhat cheesy song may help! Coming to you from Jimmy Buffett, the singer has a relaxed, island/ska like vibe to his music.  The lyrics come close to sounding like an after school special until the words “Math Sucks” are sung over and over again.  Enjoy! 🙂

Click here to listen to the song:Screen Shot 2018-02-06 at 1.41.05 PM.png

‘Math Suks’ by Jimmy Buffet Lyrics:

If necessity is the mother of invention
Then I’d like to kill the guy who invented this
The numbers come together in some kind of a third dimension
A regular algebraic bliss.

Let’s start with something simple, like one and one ain’t three
Any two plus two will never get you five.
There are fractions in my subtraction and x don’t equal y
But my homework is bound to multiply.

Math suks math suks
I’d like to burn this textbook, I hate this stuff so much.
Math suks math suks
Sometimes I think that I don’t know that much
But math suks.

I got so bored with my homework, I turned on the TV.
The beauty contest winners were all smiling through their teeth.
Then they asked the new Miss America
Hey babe can you add up all those bucks?
She looked puzzled, then just said
“Math Suks”.

Math suks math suks
You don’t even have to spell it,
All you have to do is yell it…
Math suks math suks
Sometime times I think that I don’t know that much
But math suks.

Geometry, trigonometry and if that don’t tax your brain
There are numbers to big to be named
Numerical precision is a science with a mission
And I think it’s gonna drive me insane.

Parents fighting with their children, and the Congress can’t agree
Teachers and their students are all jousting constantly.
Management and labor keep rattling old sabers
Quacking like those Peabody ducks.

Math suks math suks
You don’t even have to spell it,
All you have to do is yell it…
Math suks math suks
Sometime times I think that I don’t know that much
But math suks