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Question


Dear Mitch,

I know I'm VERY 'last-minute-ish' for this request, but this has been my first year coaching two sports on top of my usual teaching schedule in a combined middle-school/high-school in a large suburban district outside Dallas, Texas, and, well, I have no excuse worth your digital time, but would you find it in your heart to suggest something I could try with my class this afternoon that has some tie-in to this day in 1452, which was the birthday of the brilliant artist/scientist/problem-solver/inventor Leonardo Da Vinci?

Year after year I see that students of all ages are fascinated by Da Vinci, so I did pull up a few things off the internet already, just in case, but I know from visiting your site that I can always count on some fresh concept or way to apply skills that my students and I would probably never have thought of ourselves. I realize this is about as close to no advance notice as you can get, but my department head says you actually enjoy doing this kind of thing to help colleagues out of awkward jams.

Anything?

Gratefully,

Mrs. Mahlenorff

Just Outside Dallas, Texas

Answer

Dear Mrs. Mahlenorff,

I'll try!

First, though, I'd like to tell you a question that popped into my head that I thought your students might try as a quick warm-up. It's this: Since Leonardo Da Vinci was indeed born on this day in 1452, how old would he be if he were still alive today?

How old would he be in weeks?

How old would he be in days?

How old in minutes?

How old in seconds?

How old would the artist be in 'dog years'? (I believe the conversion factor is one year of a dog's life = seven years in a person's.

Those questions strike me as slightly more ordinary than the type I usually find fun. I prefer any mathematical question that connects two or more concepts or subjects that are ones most people don't often think of as naturally linked. And today, April 15th, is a perfect opportunity for such connected thinking, because not only is it the anniversary of Leonardo Da Vinci's birthday, BUT, as if that wasn't enough to celebrate in one day, today is ALSO the anniversary of the day that the very first McDonalds Restaurant opened for the world to enjoy. That miracle took place in a place called Des Plains, Illinois, and was the miracle of the year 1955.

Mathematically, one can hardly decide where to begin analyzing the seemingly infinite connections between these two nontrivial events. However, since I must eventually end this response, logic dictates that I must first begin. Somewhere. Anywhere...

I will not bother you with the details of the research grant I just received which will allow me one interrupted decade to search the Mona Lisa's foreground for hints of golden arches, nor will I make myself the envy of every Chicken McNugget fan by articulating Da Vinci's early sketches of boomerangs constructed of "poultry", which he spelled so differently that it is often just read as 'wood' or 'stone', but I will ask one mathematical question that has been concerning me for longer than I usually will admit to. It's this: Although Da Vinci's masterpiece, The Last Supper was never completed and has since withstood imperfect upkeep over the centuries, if the dishes on the table, which are difficult to make out clearly, were in fact early precursors to our modern 'happy meal', how would the wise men seated at the grand table settle the dispute emerging from some of diners fully grasping which deals are better with a large drink, regardless of their actual thirst, while not dampening the spirit of the others, who are equally wise but proudly proclaim themselves 'non-math people'?

Lastly, if a tip is in order, but rather than the standard 15% gratuity, the guests decide to increase the 15 % by a NEW 15 %, how much tip will they leave the waiter? (Be careful, because you do not just ADD 15% to 15% to get 30%. No, it's a bit more involved than that, so feel free to read it carefully.)

Finally (which comes after 'lastly') if the bill is $258.00 even, and they decide to stick to their increased tipping concept, how much gratuity will the waiter enjoy from that table on that famous evening?

Good luck!

Hope this helps,

Mitch