corticalsteelx Posted February 1, 2005 Report Share Posted February 1, 2005 I received this puzzle a few day ago and I have no clue about the answer. After shifting the inner blocks of the triangle to form a new and identical triangle one block is missing. I still get a triangle but with one block less. How can this be? EDIT: File replaced by Tormod to reduce filesize. Original was 500K!!! Link to comment Share on other sites More sharing options...
Fishteacher73 Posted February 1, 2005 Report Share Posted February 1, 2005 I have not seen this before, but one problem that comes up when looking at this diagram, is that if you find the total area of the large triange: 1/2(bh)= 1/2(13X5)=32.5 square units. When the tiangle is broken up into sub units the sum of the areas = 32 square units on both triangle neglecting the "hole". If one were to put the two tiangles together to form a rectangle, you would have an area: Area=bh = 13X5=65 square units. The sum of the sub-units in the triangles would equal 64 square units and your missing square would total up to 65 square units. :hyper: Link to comment Share on other sites More sharing options...
hefner Posted February 1, 2005 Report Share Posted February 1, 2005 It looks like some subtle fudging in the drawing of the two specimens. The hypotenuse of the bottom specimen is bowed ever-so-slightly outward, while the opposite is true of the top one. You can detect this by where the upper left corner of the #4 piece touches the hypotenuse in the bottom drawing, and compare that to the same locale in the top drawing. Link to comment Share on other sites More sharing options...
Tormod Posted February 1, 2005 Report Share Posted February 1, 2005 The solution is related to the thickness of the lines used to draw the triangle in the first place. Link to comment Share on other sites More sharing options...
Turtle Posted February 1, 2005 Report Share Posted February 1, 2005 This is sideshow trickery & has set us all back rather than advance us. :hyper: Link to comment Share on other sites More sharing options...
corticalsteelx Posted February 1, 2005 Author Report Share Posted February 1, 2005 I cut out the units and rearrange them on the graph. They fit exactly as shown. Therefore, there is not illusion or discrepantie in the drawing, I think. Probably a mathematical solution as described byFishteacher73? Link to comment Share on other sites More sharing options...
Turtle Posted February 1, 2005 Report Share Posted February 1, 2005 I understood Fish to say there's a problem here. In geometry, a construction, drawing lines or cutting them, is never more than a guide. This is meant to deceive & confuse. :hyper: Guess it works! Link to comment Share on other sites More sharing options...
Fishteacher73 Posted February 1, 2005 Report Share Posted February 1, 2005 One must always assume that the diagram is not accurate. Lines technically have no value, but ion a drawing they do. I do not think the drawing is distorted in any way, but the lines take up space and "consume" part of the area when you brake it up into pieces. This is where the "extra" square unit came from. Link to comment Share on other sites More sharing options...
Tim_Lou Posted February 2, 2005 Report Share Posted February 2, 2005 looks at the slope of the line, its 5/13, so, when moving the blocks to their final positions, they are not supposed to fit the picture... look at the corners and such, they dont fit exactly. Link to comment Share on other sites More sharing options...
Tim_Lou Posted February 2, 2005 Report Share Posted February 2, 2005 take a look at the picture, i circled some important spots... the final triangle isnt quite the same as the one before... take a look. Link to comment Share on other sites More sharing options...
pgrmdave Posted February 2, 2005 Report Share Posted February 2, 2005 The slopes of the two smaller triangles aren't the same - one is 3/8, one is 2/5 - there is no way that they could form a triangle. Link to comment Share on other sites More sharing options...
hefner Posted February 2, 2005 Report Share Posted February 2, 2005 The slopes of the two smaller triangles aren't the same - one is 3/8, one is 2/5 - there is no way that they could form a triangle.Precisely what I found as well! Hence my answer in post #3 above was the correct one: the hypotenuse bulges somewhat in the lower drawing, and is a tad concave on the top specimen. :hyper: Afterthought: that puzzle is one of the kewlest tantalizers ever!!! Link to comment Share on other sites More sharing options...
Tim_Lou Posted February 2, 2005 Report Share Posted February 2, 2005 mystery solved :hyper: Link to comment Share on other sites More sharing options...
bumab Posted February 2, 2005 Report Share Posted February 2, 2005 Looks to me as if the angled side of the triangle is slightly bowed in, thus the slopes are slightly different. That's why the two triangles, when switched, form a different slope. I bet that's where the extra space comes from, the difference in the non-linear edge Link to comment Share on other sites More sharing options...
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