Despite appearances, the top object isn't triangle, and so there is no paradox that needs to be resolved.
(If it were a triangle, then the red and green triangles would be similar, and so the ratios of their corresponding legs would be the same - but they're not.)
For the top triangle: If the grid is as it seems (congruent squares sharing verticies with neighbors), and if the edges of the triangles go through the points (verticies of the squares) that they seem to, then my post's reasoning was correct; despite appearances, the hypotenuse cannot be a straight line.
If those assumptions are wrong, then the top object might be a triangle, but also our inferences about what the grid "tells us" become suspect, thus removing the seeming conundrum.
If you don't like the plane geometry, then you can do the same thing by analytic geometry: With the above assumptions that everything about the grid & "lines" is as it seems, set up a coordinate system for the top "triangle": the origin is the lower left-hand corner, x-axis is horizontal, y-axis is vertical, and each square's side is length 1. Then the "hypotenuse" goes through A(0,0), B(8,3), and C(13,5). But the AB slope is 0.375, but for BC it's 0.4. Thus {A,B,C} aren't collinear.
@VeryEvilPettingZoo if it isnt a triangle what is it?? certainly doesnt look like a square etc. and no it isnt just an irregular polygon.. silly.. "A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments." PS i love beverages
Triangles have 3 line segments. As I've shown, assuming the grid is as it appears, the "hypotenuse" is in fact *not* a line segment. Thus it has at least 4 distinct line segments. You're arguing that a demonstrably 4+ sided polygon should be called a triangle. And that *is* silly.
Either the the grid & interesction points are misleading (in which there's no conundrum to resolve), or they're as they appear, in which case it's a **FACT** that the "hypotenuse" isn't a line segment.
@VeryEvilPettingZoo actually they are both triangles its just that the gradients are different but your eyes percieve tham as the same and thats waht causes the missing hole
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13bleep 5 months ago
10/10 go to the top of the class.
ReverendFlatus 1 year ago
Despite appearances, the top object isn't triangle, and so there is no paradox that needs to be resolved.
(If it were a triangle, then the red and green triangles would be similar, and so the ratios of their corresponding legs would be the same - but they're not.)
VeryEvilPettingZoo 1 year ago 3
@VeryEvilPettingZoo three sides, right angle = right angle triangle
afee65203 1 month ago
@afee65203
For the top triangle: If the grid is as it seems (congruent squares sharing verticies with neighbors), and if the edges of the triangles go through the points (verticies of the squares) that they seem to, then my post's reasoning was correct; despite appearances, the hypotenuse cannot be a straight line.
If those assumptions are wrong, then the top object might be a triangle, but also our inferences about what the grid "tells us" become suspect, thus removing the seeming conundrum.
VeryEvilPettingZoo 4 weeks ago
Comment removed
VeryEvilPettingZoo 4 weeks ago
This has been flagged as spam show
(cont)
If you don't like the plane geometry, then you can do the same thing by analytic geometry: With the above assumptions that everything about the grid & "lines" is as it seems, set up a coordinate system for the top "triangle": the origin is the lower left-hand corner, x-axis is horizontal, y-axis is vertical, and each square's side is length 1. Then the "hypotenuse" goes through A(0,0), B(8,3), and C(13,5). But the AB slope is 0.375, but for BC it's 0.4. Thus {A,B,C} aren't collinear.
VeryEvilPettingZoo 4 weeks ago
@VeryEvilPettingZoo if it isnt a triangle what is it?? certainly doesnt look like a square etc. and no it isnt just an irregular polygon.. silly.. "A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments." PS i love beverages
afee65203 4 weeks ago
@afee65203
Triangles have 3 line segments. As I've shown, assuming the grid is as it appears, the "hypotenuse" is in fact *not* a line segment. Thus it has at least 4 distinct line segments. You're arguing that a demonstrably 4+ sided polygon should be called a triangle. And that *is* silly.
Either the the grid & interesction points are misleading (in which there's no conundrum to resolve), or they're as they appear, in which case it's a **FACT** that the "hypotenuse" isn't a line segment.
VeryEvilPettingZoo 4 weeks ago
@VeryEvilPettingZoo im still right. im always right.
afee65203 4 weeks ago
@VeryEvilPettingZoo actually they are both triangles its just that the gradients are different but your eyes percieve tham as the same and thats waht causes the missing hole
switch675 1 week ago