Geometric Transformation Puzzles(khanacademy.org)
khanacademy.org
Geometric Transformation Puzzles
https://www.khanacademy.org/math/recreational-math/brain-teasers/e/transformation-puzzles
5 comments
I took me forever to figure out how to execute the reflection (which is to click on the arrows that point to the dash-line after you position it by dragging.) But it might be from being dropped in the middle instead of going through the sequences.
Yeah, not intuitive at all. Why do you have to click the reflection button if reflection is the only operation you have? There seems to be no response from the interface when you click the arrow if you have it poorly placed. It would be much nicer if it left the reflection line there in a different color and created a new line in a different color so you could see what happened more clearly.
Christ, thank you, I thought Ghostery was blocking something important or something.
Thanks for the feedback!
The undo button thing would be a huge improvement; I'll fix that. (Also, if you do two transformations that cancel each other out, it will notice and remove both rather than adding two. So you can actually undo a reflection by clicking the reflector again.)
As some other comments have pointed out, you might have seen the text based dilation, which is used for one of the problems for a specific reason :). The dragging dilation tool is far from perfect, but is a bit closer to what you described.
The undo button thing would be a huge improvement; I'll fix that. (Also, if you do two transformations that cancel each other out, it will notice and remove both rather than adding two. So you can actually undo a reflection by clicking the reflector again.)
As some other comments have pointed out, you might have seen the text based dilation, which is used for one of the problems for a specific reason :). The dragging dilation tool is far from perfect, but is a bit closer to what you described.
Agreed, though they did the dilation interface idea basically for the third puzzle, and it didn't feel significantly better. I would like to see maybe the math for the current transformation, as it would make it feel more like a puzzle that I could solve and work out an elegant solution to, rather than a guess and check thing where I eventually get it after some ugly combination of steps.
Yeah the second problem was easy to solve with a dilation of -1 about the origin, but then I couldn't do a negative number through the drag interface.
That frustrated me so much. Like I thought if I dragged through the point from one side to the other I could do a negative dilation and maybe the color would change to indicate that or something, but it just didn't work.
the click and drag dilation is introduced in later puzzles
I found puzzles involving dialation to be quite annoying.
Consider this solution for the third puzzle of Transformation Puzzles 2:
Consider this solution for the third puzzle of Transformation Puzzles 2:
Reflection over the line from (1.5,-1.5) to (-1.5,1.5)
Dilation of scale 256 about (2.5,2.5)
Reflection over the line from (1.5,-1.5) to (-1.5,1.5)
Dilation of scale 1/256 about (2.5,2.5)
First, I'm very sorry about that!
Second, wow, a scale factor of 256! Off the top of my head it might be numerical error building up. If that's the case, I'm very sorry. (It's also sometimes possible to get infinitesimally close to the target without technically reaching it mathematically, in which case the interface unfortunately looks like the answer is correct, when it's not.)
All of the puzzles are solvable with dilations of scales only 2 or 1/2.
Second, wow, a scale factor of 256! Off the top of my head it might be numerical error building up. If that's the case, I'm very sorry. (It's also sometimes possible to get infinitesimally close to the target without technically reaching it mathematically, in which case the interface unfortunately looks like the answer is correct, when it's not.)
All of the puzzles are solvable with dilations of scales only 2 or 1/2.
I thought these were really great, and the UI was nice too, once I figured it out. Some minimal instructions might be helpful for someone thrown directly into the puzzles without having gone through whatever led up to them.
I ran into a situation where it seemed like there was no viable solution which kept the figure under manipulation within the visible bounds at all times, so it was made more difficult by having to visualize where it went offscreen in order to keep track of what I had to do next. It's entirely possible that I could refactor the operations into something that kept it onscreen the whole time, but I couldn't find it, so I really wanted a way to zoom out or pan around, or at least some encouragement like "this should be possible without the shape leaving the visible area." Maybe giving the user the ability to zoom out but also drawing a bounding box that shows the space you're expected to do the transformation in would help.
I ran into a situation where it seemed like there was no viable solution which kept the figure under manipulation within the visible bounds at all times, so it was made more difficult by having to visualize where it went offscreen in order to keep track of what I had to do next. It's entirely possible that I could refactor the operations into something that kept it onscreen the whole time, but I couldn't find it, so I really wanted a way to zoom out or pan around, or at least some encouragement like "this should be possible without the shape leaving the visible area." Maybe giving the user the ability to zoom out but also drawing a bounding box that shows the space you're expected to do the transformation in would help.
Given the solution, a fish was a great choice of shape.
Spend 30 minutes building something in OpenSCAD and you will be a wiz at this game.
I'm stuck on part 2 #1.
It's a great interactive puzzle either way. I imagine that making it more highly interactive would be a great way to help kids get better at spatial reasoning.