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Excellent question... You speak of things I never heard of and I'm curious for the answer and explanation. So after a quick Google, descriptive geometry is the same as or similar to my Freshman Engineer (101) graphics class back in the "Dark Ages". I am starting to grasp your question, but the pi 1 and pi 2 are confusing me, sorry. Apparently, I need me some more Google. Later maybe, if I find something.
Sorry to have to tell you this, but the wording of your question is so unclear that I have no idea of how to help you. In what content did this question (or these questions) arise? What, specifically, are you hoping to learn? What do "pi 1" and "pi 2" signify?
From where did you get this homework problem? I'd suggest you go back to that source and ensure that you have copied down and typed in here every bit of the instructions and any other information presented with this problem.
Thanks @mathmale I'm kind of glad some body else found this confusing. :)
@mathmale , @retirEEd , It's descriptive geometry : using the words "pi one " , "pi two" is common as it's the standard name for the projection planes. |dw:1450038530190:dw| As the plane pi-1 rotate 90 degrees we will get |dw:1450038635642:dw| What am asking is , if I projected a triangle in a plane from a plane like this |dw:1450038714127:dw| or whatever shape will it still has it's properties. |dw:1450038805416:dw| -The second question I wanna know where exactly , should i use auxiliary planes , the one of the few reasons I know is to find the true length. |dw:1450038887952:dw| I am looking for the rest.
It does seem, that google leaks knowledge about this subject only a few links.
Thanks for the education and the answers.
@retirEEd , I am looking for a good answer xD
Hope there are others on OpenStudy who can help you. I encourage you to re-read your original post and ask yourself how you could have presented your question more clearly. Otherwise your time, as well as that of others, is lost as we try to figure out your message and determine what your question actually is.
I sure you know the answer; however, I will play along. You have a square, with the properties of a square, four congruent lines at right angles to each other. No matter what plane you look at it in, it is still a square. |dw:1450051352040:dw| As for Auxiliary view, use them to show how it really looks, as in your last drawing.
@retirEEd , Nice but the square will have it's properties only in two cases : if it's a frontal or horizontal otherwise, only parallel side will remain the same. Not always , In some cases projection can turn the square into triangle or parallelogram
@retirEEd , what are you currently studying ?
I thought this was a trick question. I agree a square viewed at an angle looks distorted, into a rectangular shape or even a line per my drawing. I am have trouble visualizing a triangle; however, but I trust you. The square will always be a square, but the point of view must somehow be conveyed in the drawing. A sphere not so much. Thanks for the update on the question. I knew you knew the answer.
@TrojanPoem I'm not so much studying as I am trying to relearn. After working 35 years at Texas Instruments and getting two EE degrees, while I worked there, my job went away. I couldn't cope in the new job they found for me, so I moved on. I was in a pigeon holed in a career strategy and couldn't work outside of the box. I had always saved well, into my 401K, so at the ripe old age of 56, I decided to take my retirement. After 18 months of resting and self loathing, I decided I to re-hone my math skills and possibly volunteer as a math tutor. I always struggled through the math at university, because it was so fast and with too much competing course work. Hence, coming to this site and try to re-fresh and to learn the new ways of teaching math. And I have to admit, I have found some nice new tricks here. I'm sure this is more info than you ask for, but thanks for asking.