Creating a Ham Sandwich Cut Interactive Applet Necklace Thieves References Main Page

Duality
 
  • Below is the table of conversions that I used to create the dual of the set of points.

In primary

 In Dual
A point in the dual becomes...  

a line in the dual,  where the x coordinate is the slope and the y coordinate becomes the y-intercept

 
(a , b) y = a * x + b
A line in the dual becomes...  

a point in the dual, where the negative of the slope is the x coordinate and the y-intercept is the y coordinate.

 
y = m * x + b

(-m, b)

 

Properties of the Dual
 

1. A line that is above a point in the primary, is the corresponding point that is above the line in the dual.

 

Primary

Dual

  

2. Points that are co-linear in the primary, will be lines that all intersect at one point in the dual.

 

Primary

Dual
 

3. The vertical distance between a point and a line is preserved.

 

Backgrounds taken from