PEANUT BUTTER AND BANANA SANDWICH

2 slices of bread

peanut butter

banana, sliced

Spread peanut butter on bread. Lay banana slices on, mash with a fork until the two have amalgamated. Close sandwich. Eat.

**Mary:** "I think you should just let people know that depending on the ripeness of the banana, the consistency of the peanut butter, and the gumption of the bread, the bread could potentially get squished, and this is not necessarily bad unless you are trying to be Martha Stewart. But I think the charm of making the sandwich is in the mashing of the banana on the peanut butter on the bread. It is a joyful experience. If someone wants to they can mash it in a bowl, but not only does that dirty a bowl, it greatly decreases the sensual experience of making the sandwich."

**Joe:** "While browsing thru the online cookbook, i was struck when i saw the peanut
butter and banana sandwich. i have never done the mashing of the banana
into the peanut butter step, and i do not ever remember mom doing this (if
she ever made them for us...i do not remember). but reading mary's comment,
it seems a very crucial element of the sandwich. when making this delicacy,
i never squish the bananas. the challenge is cutting the banana slices all
the same width so that the sandwich is not lumpy because one banana is
thicker than the others. also, the arranging of the banana slices on the
bread becomes crucial...so that every spot is covered. also, i always try
to use the entire banana, so you have to cut the correct number of
equi-width slices so as to fill the whole area sandwich perfectly. the
stickiness of the peanut butter prevents the banana slices from slipping out
of the sides of the sandwich. i quite enjoy tasting the two distinct
textures of peanut butter and banana. i could not imagine enjoying the two
squished together because then it would just be a goopy-goop sandwich."

"the peanut butter banana sandwich, by the way, was one of elvis's favorite meals. i do not know how he prefered it to be made, but i would guess without the squishing together."

**Liz:** "i too would have to disagree with the mashing together of banana and peanut
butter (perhaps this has been a habit acquired making sandwiches for liam?).
definitely sliced bananas was how i remember making them and the way to
go."

**Anne:**Your efforts to attain the ideal sandwich experience are to be commended. The challenge which you have taken upon yourself is great. Regardless, you may consider these benefits of the _traditional_ Sustar peanut butter and banana sandwich:

1) The space-filling challenge of making this sandwich need not be a stress in your life.

2) Mashing the bananas does cover every spot of the bread better than a layout of circular slices is ever capable of. [At most, a regular arrangement of circular banana slices can cover no more than about 1-((sqrt(3)-pi/2)/sqrt(3)) = 91% of the sandwich, unless the banana has unusually pointy ends. - Walter]

3) A goopy-goop texture is something that renowned French chefs often strive for in their dishes. You do not need to be afraid of the goopy-goop quality that IS the nature of peanut butter and bananas.

Thank you for your input to the Sustar Online Cookbook. Let us know what you decide."

**Dad John F.** "The effectiveness of coverage and the change is texture is very important in
eating. When we were growing up, it was important to slice the pickles in
the long dimension to avoid the pitfalls of circular coverage as pointed out
by Walter. Of course we didn't use bananas with the pickles, just the
pickles with butter on the fresh baked bread. And then there were the raw
onion sandwiches. We diced the onions, again to aviod the pitfalls of
circular coverage. Again, it was with butter on the freshly baked bread.
Radishes were cut in circular slices."

**Mom Ronnie:** "Sounds like this PB/banana question got a lot of response Joe. guess it was mary who put the recipe it and she hasn't yet responded. BUT, growing up I made and ate them with mashed bananas and possibly I made them that way for a while (for Peter and Mary?) but it does squish the bread if you mash them in place. I'm waiting for Mary's response."

**Mary:** "I do not remember commenting on the making of peanut butter banana sandwich making,
but apparently I did as it is in writing in the family cookbook. It is always good
to squish food, especially with your fingers. I do not like pnut banana sandwiches
so my opinion is meaningless."

**Joe:** "an,
how did you get the 91% coverage of bananas on a snadwich. your formulas
confused me. here is how i calculated it:

area of a square minus the area of a circle that can fit in that square. so, if we have a banana slice with a diameter of 1 inch, therefore an area of .785 inches, it would take up 78.5% of the smallest square in which it could fit (a square with 1 inch sides). because, no matter how you arrange the bananas, the extra area of bread around the individual banana slice will always be a square with sides the same length as the diameter of the banana. i'm sure that my simplfied formula is missing something, but i can't see why this also would not work for radishes...despite their non-cylindrical shape.

and, the process of slicing and arranging the bananas is not a point of stress in my life. i have mastered the process, therefore, feeling no need to moosh or be french.

still researching elvis's preference."

**Walter:** "The 91% calculation is me (Walter), not Anne. The mistake you made was assuming that the circle is in a square. Packing bananas on a square grid is not the best fit; packing them on a hexagonal grid is better. So, figure the area of a hexagon (hint: a hexagon is made of equilateral triangles), and subtract the circle.

Radishes don't tile the plane the same way, because the circles they make are not all the same size. So, a regular grid is not the optimal packing.

Side note: although hexagonal packing is optimal for circles on a 2-D plane, it does not follow that it is best for spheres in a 3-D volume, hyperspheres in a 4-D hypervolume, et cetera. The problem of figuring optimal packing in high-dimensional spaces turns out to be mathematically quite challenging."

"It is left as an exercise to the mathematically inclined reader to determine the maximum coverage attainable by slices taken from a spherical object such as a radish (as opposed to a cylindrical object such as a banana). Hint: it depends on how thick you slice the radish."

"I have never heard of radish sandwiches until now."

**Joe:** "i found out the answer to my question: How did Elvis demand his Peanut
Butter and Banana Sandwiches?

He liked them with very ripe bananas, MUSHED up, then spread on toasted wonder bread, along with the smooth peanut butter, and then...he like the sandwich fried in a skillet with melted butter. it sounds similar to mary's brilliant grilled peanut butter and jelly sandwich.

elvis, by the way, insisted on eating the sandwich with a fork and a knife. this was his favorite snack. Elvis ate these for breakfast, lunch and dinner (alongside chicken fried steak, corn bread, mashed potatoes, sweet potato pie and yes, green beans).

nonetheless, i still am sticking with the sliced bananas arranged in an efficient hexagonal model...and not fried. i will only grill my PB & Js."

Bring me back to The Sustar Cookbook.