CHRISTMAS TREE MATH FOR THE WHITE HOUSE

[mudslinger]

, Alexandria Jones and her family were on their way to Uncle William’s tree farm to find the perfect Christmas tree, and Dr. Jones
taught us about the Golden Section:

|———————A———————|————B————|


I gave you three algebra puzzles to solve. Did you try them?

• What is the exact value of the Golden Section ratio?

• If a 7-foot tree will fit in the Jones family’s living room, allowing for the tree stand and for a star on top, how wide will the tree be?

• Approximately how much surface area will Alex and Leon have to fill with lights and ornaments?

Math Adventurer’s Rule: Figure It Out for yourself
Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterwards. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you have not worked these problems yet, go back to the original post. Figure them out for yourself — and then check the answers just to prove that you got them right.


The Golden Section Ratio
To find the Golden Section ratio, remember that the length of the line does not matter. That means that we can pick a line of any convenient length. We will make our problem easier by choosing B = 1. Then the Golden Section ratio A/B will be the same as the length of A:
|———————A———————|————B————|

And that will make our Golden Section equation look like this:


Multiply both sides of the equation by A:

Now put it into standard quadratic form:

That looks better, doesn’t it? Unfortunately, this equation cannot be factored, so we will have to use the dreaded Quadratic Formula. Finally we get:

Answer: So the Golden Section ratio, which compares the long section A to the short section B (or the whole line to the long section), is approximately 1.618.
How Wide Was the Christmas Tree?
Now for the next part of the puzzle: What size was the Jones family’s Christmas tree? If the tree was pruned to the Golden Section ratio, then the height H compared to the width W should be about 1.618:

We can solve this equation for W:


Since we are being overtly American and measuring in feet, we need to handle decimals with care. One foot is 12 inches, and 0.3 will be about 1/3 of a foot, so…
Answer #1: For a 7-foot tall tree, W is about 4 feet 4 inches.
If, however, the tree was trimmed to Grandpa Jones’s rule of thumb, then:


Answer #2: For a 7-foot tall tree, that gives a width of 4 feet 8 inches.
The Golden Section makes for a slimmer tree. But with such a small difference, you can see why Grandpa preferred the simpler rule

[Griobhtha]

Mud, we told you YESTERDAY, but you dense skull keeps information from coming in, is that the tree is a live, growing tree, planted in 1978 and that GE has decorated the tree for the LAST 40 years!  Learn something!

[mudslinger]

GE IS A LEFT WING ORGANIZATION IT IS NOW WONDER THE DECORATING IS ALL FUNKED UP , JUST LIKE OBAMA'S GOVERNMENT. GE NEEDS TO LEARN SOMETHING, HOW TO DECORATE A CHRISTMAS TREE SO THAT IT MEETS THE ABOVE PROPORTIONS AND LOOKS LIKE A CHRISTMAS TREE.

[takncarabizniz]

Still Grio, I don't like the way it looks either.  Draping the tree in such a dense number of lights does nothing for it.  There is an art to making trees look right with lights and using the netting drape has never appealed to me. 
 
 

[Griobhtha]

that is ok, Takn, but IT isn't the White House's  fault.  Mud is just being obstinate.

[takncarabizniz]

I will post this again as well.
 
http://www.thenationaltree.org/timeline/
 

I think less is more and w/ such a huge tree, the lights will have enough shine to them that it's unnecessary to drape the whole thing in them...the only thing that Obama can be accused of is signing off on it and not expressing that it was overkill.  Frankly, even w/ the LED, energy savings, I am thinking there was an agreement w/ the power companies by GE to use a certain amount of power consumption so someone would make money off the deal...LOL  There's your conspiracy theory for the day...


 
 

[Griobhtha]

looks the same as 2008