Question

graph:

Answer 1

\[\left| x \right| + \left| y \right| = 1\]

Answer 2

Must be joking..

ha ha ha..

Answer 3

This will give you 4 equations..

Answer 4

really?

Answer 5

because the graph is a square.

Answer 6

it is a square

Answer 7

Yes really..

Answer 8

brb, okay so the four equations are:

Answer 9

think about what points are on the graph

Answer 10

there is my lousy picture

Answer 11

its beautiful

Answer 12

it is the unit circle

Answer 13

@satellite73 so i just put in random values of x and y?

Answer 14

well, it is the unit circle in the \(l_1\) norm in two dimensions

Answer 15

suppose \(x,y>0\) i.e. you are in quadrant I

Answer 16

aahhh

Answer 17

then \(|x|=x\) and \(|y|=y\) since they are both positive

Answer 18

so in quadrant I you have the line \(x+y=1\) or if you prefer \(y=1-x\)

Answer 19

-x and y are in quadrant 2?

Answer 20

so then the equation is y=1+x?

Answer 21

in quadrant II \(|x|=-x\) and \(|y|=y\) so yes, you get \(-x+y=1\) or \(y=x+1\) etc

Answer 22

repeat for all 4 quadrants and you will see what you get

Answer 23

great stuff

Answer 24

okay thx! :)

Answer 25

yw

Answer 26

@cwrw238 it really is the unit circle, if you define the distance between to points \((x_1,y_1), (x_2,y_2)\) as \(D=|x_2-x_1|+|y_2-y_1|\)

Answer 27

*two points

Answer 28

right - i was a confused about that

Answer 29

lol does that mean we've squared the circl?e!!! - i suppose not!