Math Is Fun Forum

Isn't the crust to bread ratio better both on diagnolly cut toast and circular toast?

this is exactly why it tastes better. lets break it down royal institute christmas lecture style. imagine the toast is a rectangle with:

width of toast = x
height of toast = y

length of crust portion of perimeter = c
length of bread portion of perimeter = b

bread to crust ratio = b/c = z

we'll ignore the thickness of the slice for the purposes of this, and assume that, when cut lengthways, the bread is always cut along the x axis.

----------------------
toast cut 'lengthways'
----------------------

c = 2(x+y)
b = 2x

z = x/(x+y)

--------------------
toast cut diagonally
--------------------

c = 2(x+y)
b = 2(x^2+y^2)^0.5

z = (2(x^2+y^2)^0.5)/(2(x+y))
= ((x^2+y^2)^0.5)/(x+y)

The z axes on the above representations are on different scales so it looks a little off. The difference between the ratios is always positive, for positive, non-zero values of x and y:

Is this correct??