Can you explain this?
Posted: Wed Jun 04, 2008 10:57 pm
Hi!
Take a look at this. Can you explain it?
Coco.
Take a look at this. Can you explain it?
Coco.
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Posted: Thu Jun 05, 2008 12:52 am
The two triangles have different gradiants.
Posted: Thu Jun 05, 2008 9:16 am
he's right that causes it
Posted: Thu Jun 05, 2008 10:20 am
Hi!
That's not precisely the explanation. Can you give some more details?
Coco.
That's not precisely the explanation. Can you give some more details?
Coco.
Posted: Thu Jun 05, 2008 10:37 am
hard to tell details about it cause you got to change the things in your mind but it is true
Posted: Thu Jun 05, 2008 4:03 pm
isnt it just the arrangement?
Posted: Thu Jun 05, 2008 5:43 pm
Hi!
No, Nosh, if you compare the coloured figures (i.e. count the length of their sides in squares), you will see that they still appear to be the same as before.
The same counts for the gradient of the big triangle, Wullf. Otherwise, at least one side would be longer.
Coco.
No, Nosh, if you compare the coloured figures (i.e. count the length of their sides in squares), you will see that they still appear to be the same as before.
The same counts for the gradient of the big triangle, Wullf. Otherwise, at least one side would be longer.
Coco.
Posted: Thu Jun 05, 2008 5:52 pm
its so formula I believe I have seen this before..
I believe it goes like this..
you have to count the squares..
the green triangle has 2x5
then you have to divide it to get to the gradiants..
2/5 is 0.4
the red triangle has 3x8 wish results in 0.375 if u divided 3/8
meaning that the smaller one.. even though being smaller has larger gradiants.. so the hole appears becuze when switched around.. it makes up for that 0.025 thats missing..
if you'd be a smart guy u cud probably calculate that the square amount to 0.025 gradiants..
I believe it goes like this..
you have to count the squares..
the green triangle has 2x5
then you have to divide it to get to the gradiants..
2/5 is 0.4
the red triangle has 3x8 wish results in 0.375 if u divided 3/8
meaning that the smaller one.. even though being smaller has larger gradiants.. so the hole appears becuze when switched around.. it makes up for that 0.025 thats missing..
if you'd be a smart guy u cud probably calculate that the square amount to 0.025 gradiants..
Posted: Thu Jun 05, 2008 6:36 pm
Hi!
Right, Ghost. To make it a little clearer: The gradient is defined by how many steps you must go up (or down) at the Y axis when you go one step to the right on the X axis.
For the dark green triangle, the gradient is 5 steps (squares) to the right and 2 steps up. So for one step to the right, you would have to go 2/5 = 0.4 steps up. The gradient therefore is 0.4.
For the red triangle, the gradient is 8 steps to the right and 3 steps up. So for one step to the right, you would have to go 3/8 = 0.375 steps up. The gradient therefore is 0.375.
In both figures, the hypotenuses of both triangles are connected, which, due to the different gradients, results in a kinked line (i.e. it is not really straight). This means that in the point where the dark green and the red triangles touch, the angle is not equal to 180 degrees.
In the upper figure, the outer angle is smaller than 180 degrees and in the lower figure (where the dark green and the red traingles exchanged their positions), the outer angle is bigger than 180 degrees.
So if you placed the upper figure on top of the lower one (and made it half-transparent), you could see the difference. It would in fact look like the missing square (the white one in the lower figure) if you picked its upper right and lower left corners and streched them to the upper right and lower left corners of the entire big triangle.
Case cleared.
Coco.
P.S.: Wulff probably meant the same, but it was way too vague for an explanation.
Right, Ghost. To make it a little clearer: The gradient is defined by how many steps you must go up (or down) at the Y axis when you go one step to the right on the X axis.
For the dark green triangle, the gradient is 5 steps (squares) to the right and 2 steps up. So for one step to the right, you would have to go 2/5 = 0.4 steps up. The gradient therefore is 0.4.
For the red triangle, the gradient is 8 steps to the right and 3 steps up. So for one step to the right, you would have to go 3/8 = 0.375 steps up. The gradient therefore is 0.375.
In both figures, the hypotenuses of both triangles are connected, which, due to the different gradients, results in a kinked line (i.e. it is not really straight). This means that in the point where the dark green and the red triangles touch, the angle is not equal to 180 degrees.
In the upper figure, the outer angle is smaller than 180 degrees and in the lower figure (where the dark green and the red traingles exchanged their positions), the outer angle is bigger than 180 degrees.
So if you placed the upper figure on top of the lower one (and made it half-transparent), you could see the difference. It would in fact look like the missing square (the white one in the lower figure) if you picked its upper right and lower left corners and streched them to the upper right and lower left corners of the entire big triangle.
Case cleared.
Coco.
P.S.: Wulff probably meant the same, but it was way too vague for an explanation.
Posted: Thu Jun 05, 2008 7:02 pm
i know it only maths lesses where so long ago i forgot
but we where a bit right it's cause the triangels got diff size, and also diff amounts of open space @ the diagonal line
that it wont come out the same
and then you got that maths formula or yours
but we where a bit right it's cause the triangels got diff size, and also diff amounts of open space @ the diagonal line
that it wont come out the same
and then you got that maths formula or yours