Original math poetry by MathDude !!! A single poem is featured below but there's plenty more to test your limits for Mathmania or groaners set to prose !! You'll find a list of other math poems ...and more ... at the end of this page ... 'attitude' poems and puzzles. The featured poem is among them ...a list that will grow as the muse hits me. The inspiration for the poem below was my better 3/4'ths (used to be my better half but she increased in value). She habitually samples my food. Couldn't count on getting my morning turnover all to myself so I designed the nefarious plot detailed in the poem. Enjoy !!!
Breakfast is my favorite meal
Especially if I cut the following deal;
To share a turnover with my spouse. It’s sliced in half, yet I play the louse.
A generic turnover forms half a square or box. I’ll use my math to play the fox.
Half the pastry she still will get, but she’s cheated with the following fix.
Instead of cutting it the ‘normal’ way
In which two smaller half boxes are formed, I may
Along another line cut this morning wedge
Which parallels the longest edge.
Her piece now contains the turnover’s fold. My piece most of the filling will hold.
In this fashion I retain the fruit for which I lust,
While she gets naught but flakes and crust
Assume this ruse will work but once. She’s given me this without a fuss.
Is she being nice or playing the dunce?
Compute the width of her fruit-starved piece. Recall it’s bordered by cut and crease.
By my warped standards the deal was fair – proving that I can do this at least,
While on my ill-gotten pastry I will now feast!
And now the solution for which I know you are breathlessly awaiting ...
It will simplify the problem by assuming the thickness is uniform and equate the area of the small red triangle to ½ of the area of the original turnover.
I let the legs of the original turnover have length 1. I’ll find all other lengths in terms of this length.
Therefore, the cut is made ~ 7/ 10 thsof the turnover leg, measured from the right angle.
The trapezoidal piece’s sides are ~ 3/10 ths of the turnover length.
Can we find the value of c and w in the pic?
Recall we used the fact that the triangles were similar to let the red triangle have equal legs x.
Since the isosceles right triangle has sides in the ratio 1 : 1 :, the side c can be found.
à = = 1 ( exactly as long as the original turnover’s leg)
w is found by equating the trapezoid area to ½ of the original turnover’s area again.
==> ==> w is ~ 1/5 th of the length of the original turnover’s leg.
The assumption of uniform thickness is not truly justified. However, without this simplified model, I wouldn’t be able to use this to teach (or torture) you about similar triangles. More Poetry and other stuff ...
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