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How? Please God someone explain!
datalas:
--- Quote from: Lewis.J.P_1987 on May 06, 2009, 22:44:45 ---I don't want to sound thick. However, I do not see how that much area could be gained from that tiny slither? :huh:
--- End quote ---
Blame Pythagoras :)
V8MoneyPit:
--- Quote from: auf_wiedersehen_pet on May 06, 2009, 22:07:26 ---Got it.
The overall shape of the triangle is there to confuse. It's actually a quadrilateral. Shifting the shapes about moves the upper edge further upwards creating the space in the bottom drawing.
:lol: :lol:
--- End quote ---
Err.... how? The edges are the same number of squares in both cases. Or am I being thick? (Answers on a post card in reply to that question!!)
generation-x:
im with steve on this im afraid :cry:
Saffy:
--- Quote from: V8MoneyPit on May 07, 2009, 10:37:27 ---
Err.... how? The edges are the same number of squares in both cases. Or am I being thick? (Answers on a post card in reply to that question!!)
--- End quote ---
bare in mind...Both diagrams use the exact same shapes, same size everything, no tricks. But you are not looking at a true triangle in the first diagram arrangement either. As said "Draw a straight line from the top point to the bottom left point" you will see that the two shapes there do not form a flat line, so it's not a real triangle (a real triangle has 3 sides and your looking at 4!). If a prefect best fit triangle is drawn around the both diagrams then you will see that BOTH diagrams will have the same areas of that gap exposed but in the first diagram that area is spread thinly along the non flat upper most face. That tiny slither might not look much but it is in fact the same area as the gap in the second.
DoubleTop:
I found it easier to explain it when looking at the two triangles.
Let's look at ratios to show the 'entire' shape isn't a triangle.
The smaller triangle is 5across2high
The second triangle is 8across3high
So, to make these comparable in math, we make the denominator the same, making the ratios
15/6 & 16/6.
So the key thing here is that the first image as stated before is NOT a complete triangle, as shown by the line 'test'. And yes that little simple ratio and clever arrangement is enough to make the extra 'hole' appear, the two shapes are NOT comparable at all. A slight trick on the eye, but in my head quite easy to show why the gap appears.
To put into some amusing 4x4 related terms, the ascent is steeper on one of the triangles ;)
DT.
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