fredreload Posted September 6, 2016 Share Posted September 6, 2016 So this is an equation I found with interesting properties. Pretty much x+y=z and x-y=z are linear equations of 2 equations 2 unknowns. If you solve for this equation you get x=z and y=0. Now I haven't got a chart for x-y=z, Google shows the x+y=z chart but not the other one, if you have it please show me. Now for z=(x+y)/(x-y) it generates an interesting chart in google, same goes for z=(x-y)/(x+y). I'm not sure if they are off by 180 degrees or simply upside down. Now when you multiple the two together you get z^2=1 which is z=1 not z=0. This seems to be an interesting property and if someone can give me an explanation on this it would be cool. To sum up: 1. Get me a chart for x-y=z 2. z=(x+y)/(x-y) and z=(x-y)/(x+y) looks interesting, when you multiply them together you get z=1, why is that and what does that mean? Link to comment Share on other sites More sharing options...

Sensei Posted September 6, 2016 Share Posted September 6, 2016 (edited) Isn't (x+y)/(x-y)*(x-y)/(x+y) equal to LaTeX: [math]\frac{x+y}{x-y}*\frac{x-y}{x+y}[/math] ?? Maybe some parenthesis missing somewhere? Which is equal to: [math]\frac{x+y}{x+y}*\frac{x-y}{x-y}[/math] [math]1*1[/math] [math]1[/math] (as long as no division by 0) f.e. if I make OpenOffice SpreadSheet with A1=1000 B1=500 and C1=(A1+B1)/(A1-B1)*(A1-B1)/(A1+B1) Result is 1. If I make A1=B1=1000 f.e. OpenOffice complains there is division by 0. Now for z=(x+y)/(x-y) it generates an interesting chart in google, same goes for z=(x-y)/(x+y). I'm not sure if they are off by 180 degrees or simply upside down. They will be z'=1/z or z'=z^{-1} Edited September 6, 2016 by Sensei Link to comment Share on other sites More sharing options...

fredreload Posted September 6, 2016 Author Share Posted September 6, 2016 They will be z'=1/z or z'=z^{-1} Hi Sensei, can you clarify on this one? Did you take the derivative or something? I know my equation becomes z=1, I'm just not sure why that is the case. If you take a look at z=(x+y)/(x-y) it looks like a spiral, so how come a spiral multiplies by another spiral becomes z=1? Also get me a chart on x-y=z, many thanks Link to comment Share on other sites More sharing options...

elfmotat Posted September 6, 2016 Share Posted September 6, 2016 (edited) I know my equation becomes z=1, I'm just not sure why that is the case. If you take a look at z=(x+y)/(x-y) it looks like a spiral, so how come a spiral multiplies by another spiral becomes z=1? Because (A/B)*(B/A) = (A/A)*(B/B) = 1*1 = 1. Try it out with numbers. If you have [(x+y)/(x-y)]*[(x-y)/(x+y)], pick random numbers for x and y. For example, x=6 and y=2: [(6+2)/(6-2)]*[(6-2)/(6+2)] = [8/4]*[4/8] = [2]*[1/2] = 1. Also get me a chart on x-y=z, many thanks https://www.google.com/search?q=z%3Dx-y+plot&rlz=1CASMAE_enUS631US631&oq=z%3Dx-y+plot Edited September 6, 2016 by elfmotat Link to comment Share on other sites More sharing options...

mathematic Posted September 6, 2016 Share Posted September 6, 2016 With different parentheses it could mean [latex] (\frac{x+y}{x-y})^2[/latex] Link to comment Share on other sites More sharing options...

elfmotat Posted September 7, 2016 Share Posted September 7, 2016 With different parentheses it could mean [latex] (\frac{x+y}{x-y})^2[/latex] But it's clear from the context of his post that that's not what he meant. 1 Link to comment Share on other sites More sharing options...

fredreload Posted September 7, 2016 Author Share Posted September 7, 2016 (edited) With different parentheses it could mean [latex] (\frac{x+y}{x-y})^2[/latex] It looks really cool, looks like a portal or some sort, got any explanation for it ? On another note my equation becomes (x+y)(x-y) on top and bottom, which looks like a saddle Edited September 7, 2016 by fredreload Link to comment Share on other sites More sharing options...

deesuwalka Posted October 24, 2016 Share Posted October 24, 2016 (edited) [latex] \frac{x+y}{x-y}\times\frac{x-y}{x+y} [/latex] [latex] =\frac{\not x+\not y}{\not x-\not y}\times\frac{\not x-\not y}{\not x+\not y} [/latex] [latex]= 1 \times 1[/latex] [latex]= 1 [/latex] Edited October 24, 2016 by deesuwalka Link to comment Share on other sites More sharing options...

Country Boy Posted October 26, 2016 Share Posted October 26, 2016 [latex] \frac{x+y}{x-y}\times\frac{x-y}{x+y} [/latex] [latex] =\frac{\not x+\not y}{\not x-\not y}\times\frac{\not x-\not y}{\not x+\not y} [/latex] [latex]= 1 \times 1[/latex] [latex]= 1 [/latex] Provided neither x- y nor x+ y is equal to 0. That is, provided neither x= y nor x= -y. If x= y or x= -y, the expression is not defined. Link to comment Share on other sites More sharing options...

mathematic Posted October 26, 2016 Share Posted October 26, 2016 It looks really cool, looks like a portal or some sort, got any explanation for it ? On another note my equation becomes (x+y)(x-y) on top and bottom, which looks like a saddle [latex](x+y)/(x-y)*(x-y)/(x+y) could = (x+y)/[(x-y)^2/(x+y)][/latex] Link to comment Share on other sites More sharing options...

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