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What is the total area in blue knowing that the area of the large triangle is 1?

 

 May 17, 2020
 #1
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LOOKs like  1/3

 May 17, 2020
 #2
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What is the total area in blue knowing that the area of the large triangle is 1? 

 

I'm not sure there's enough information provided to make the following assumption, but here goes. 

The dimensions of each smaller triangle appear to be half the height and half the base of the previous. 

I haven't a formal proof for this assumption, but I did try to measure with a ruler against my computer screen. 

So, basing the following on the preceding... 

 

If the assumption is correct, then the area of the largest blue triangle is one-fourth.

Then, the area of each smaller blue triangle is one-fourth the area of the previous, 

 

I don't know how to write this in mathematical notation, but 1/4 + 1/16 + 1/64 + 1/256 and so on. 

 

The total of (1/4)n where n=1, 2, 3, 4, and continuing forever. 

 

 May 17, 2020
 #3
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Sorry I didn't take higher maths and didn't know the terminology, so I tried to learn it.  I learned that what I was trying to say was "sigma sum" and I found an online sigma sum calculator on the internet.  Using my numbers, the answer comes out to 0.3333··· in other words, the same as Electric Pavlov's answer.  So how come EP gets two positive hearts (so far) and I get a negative?  Can somebody explain that to me? 

Guest May 17, 2020
 #4
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If there's some way to prove that the three triangels in each row are equal, then there's three triangels in each row and one of them is blue.  Therefore the blue triangels are 1/3 of the large one.  Does that make sense? 

 May 17, 2020

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