Geometry Archives - Page 4 of 4

Math Resources (in the time of COVID)

Calling all students, teachers, and parents! As everyone is stuck at home during a global pandemic, now is a ~~great~~ time we are all forced to try and understand math (and our sanity level) a little bit more. Well, I may not be able to help you with the keeping sanity stuff, but as far as math goes, hopefully, the below math resources offer some much needed mathematic support.

All jokes aside I hope everyone is staying safe and successfully social distancing. Stay well, math friends! 🙂

Kahn Academy: The same Kahn Academy we know and love still has amazing videos and tutorials as usual, but now they also have a live “homeroom” chat on Facebook LIVE every day at 12:00pm. The chats occur daily with Kahn Academy founder Sal and at times feature famous guests such as Bill Gates. Click the link below for more:

Khan Academy Homeroom

Study.com: In a time when companies are being more generous, Study.com is here for us as they offer up to 1000 licenses for school districts and free lessons for teachers, students, and parents. Check out all the education freebies here:

Study.com

Math Planet: If you’re looking for free math resources in Pre-Algebra, Algebra, Algebra 2, and Geometry then you will find the answers you need at Math Planet. All free all the time, find their website here:

MathPlanet

MathSux: Clearly, I had to mention MathSux, the very site you are on right now! Check out free math videos, lesson, practice questions, and more for understanding math any way that works for you!

MathSux

What is your favorite educational site? Let me know in the comments, and stay well! 🙂

Volume of a Cone: 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 almost cone-like structure? It seemed like the best way to estimate the volume here, was to use the formula for the volume of a cone!

What do you think the Volume is?

Volume of a Cone:

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

We can find the radius and height based on the given information above. Everything we need for our formula is right here!

Now that we have our information, let’s fill in our formula and calculate!

Extra Tip! Notice that we labeled the solution with feet cubed , 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 ()

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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 calculating! 🙂

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Looking to apply more math to the real world? Check out this post on the Golden Ratio here!

Intersecting Secants: Geometry

intersecting secants theorem

Hey math friends! In today’s post, we are going to go over the Intersecting Secants Theorem, specifically using it to find the piece of a missing length on a secant line. We are also going to see proof as to why this theorem works in the first place!

Just a warning: this blog post contains circles. This usually non-threatening shape can get intimidating when secants, chords, and tangents are involved. Luckily, this question is not too complicated and was also spotted on the NYS Regents. Before looking at the questions below, here is a review on different parts of a circle. Pay close attention to what a secant is, which is what we’ll be focusing on today:

Think you are ready? Let’s look at that next question!

What information do we already have? Based on the question we know:

Screen Shot 2018-12-25 at 12.54.24 PM.png

*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 remember having questions is a good thing!

If you’re looking for more on intersecting secants, check out this post here for practice questions and more!

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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!
The Golden Ratio

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?
(Answer: Each previous two numbers are added together to find the next number.)

The Golden Rectangle: The 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:

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

Then drew another golden rectangle within that golden rectangle?

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

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:

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!

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!

Don’t forget to connect with MathSux on these great sites!

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Looking to learn more about math phenomenons found in the real world? Check out this article on fractals! And if you want to learn about more sequences, check out the link here!