A MATHEMATICAL DIVERSION FOR TRAVELERS AND PEOPLE WHO EAT PIZZA

Having just returned from a trip to Colorado, and looking at the new totals for my lifetime flight milage (365,399), I wondered what would be the equivalent number of trips around the world I travelled in those miles.

So here's a little rough math for my aging intellect and yours...

Roughly speaking, the EARTH is 7,926 miles in diameter at the equator, making its circumference, approximately 24,900 miles. (Note that this number is actually pretty easy to remember if you use a little gonzo approximating - that there are 24 time zones on the planet and each is about 1,000 miles wide.)

And if you were in a rental car (with unlimited mileage) driving on the surface, in a straight line trip, ignoring hills, valleys and detours, and the unpaved section in the oceans where that car you rented doesn't float and would need a few tanks of gas, but you already passed the sign in Patagonia that said, "NEXT STATION 4,320 MILES", it would be pretty easy to figure out.

Oh yes, and the pirates. You want to avoid the pirates !

But the real issue is, how far is a trip around the world if one is in an airplane? At let's say for convenience, an average of 25,000' above the ground. On that airplane ride, traveling about 5 miles above the surface, you have significantly enlarged the circle that describes your trip.

Or have you?

How much longer has your trip become ?

a. 30 miles
b. 300 miles
c. 3000 miles
d. all of the above (summed)

The answer might not be surprising to you, but it was to me. The trip distance around the world is only 30 miles longer in an airplane at 25,000' than in a car on the surface.

Do the math: The circumference (C) of the earth is calculated using our old grade school mathematical formula... C = πd.

With d= diameter = 7926 miles, and at an additional 25,000 feet (or 4.734 miles), added twice (for the diameter), becomes (7926 mi. + 2*4.734) or 7,935 miles (and a bunch of decimals),

the new circumference C' = π[3.14159 etc] * d' [7935 mi] = 24, 930 miles.

An addition of a mere 30 miles.

And the answer is, 14.657 times around the world.

This may not be interesting to you, but we can use this same math for something that applies to you and me in our daily (or at least weekly) lives.... PIZZA !

Let's say you're in a restaurant and you want to know which is a better deal, the 12" pizza for $12 or the 16" pizza for $16.

Same math, different formula because when you eat pizza, you eat not just the DIAMETER, but you eat the AREA. (Or maybe you don't eat the diameter because your mama told you it would make your hair curly - but let's ignore this for now.)

The area of a circle is πr**2 (pi-r-squared), where r is the radius (= 1/2 diameter) and π is our old friend.

12" pizza = 6" radius

Area = π*36 (or 36π)

16" pizza = 8" radius

Area = π * 64 (or 64π)

Without going any further, you can see that the 16" pie puts a lot more tomato and cheese into your belly (or better still, leftovers in your freezer) for that extra $4. And IF you looked at the numbers and said it was twice as big, you'd be close enough,. Perhaps we could even say you were in the smart man's ball park. The actual numbers are: 78% more pie for 33% more money. A good deal.

And you did the pizza math without a need to remember that the value of π is 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959 5082953311 6861727855 8890750983 8175463746 4939319255 0604009277 0167113900 9848824012 8583616035 6370766010 4710181942 9555961989 4676783744 9448255379 7747268471 0404753464 6208046684 2590694912 9331367702 8989152104 7521620569 6602405803 8150193511 2533824300 3558764024 7496473263 9141992726 0426992279 6782354781 6360093417 2164121992 4586315030 2861829745 5570674983 8505494588 5869269956 9092721079 7509302955 3211653449 8720275596 0236480665 4991198818 3479775356 6369807426 5425278625 5181841757 4672890977 7727938000 8164706001 6145249192 1732172147 7235014144 1973568548 1613611573 5255213347 5741849468 4385233239 0739414333 4547762416 8625189835 6948556209 9219222184 2725502542 5688767179 0494601653 4668049886 2723279178 6085784383 8279679766 8145410095 3883786360 9506800642 2512520511 7392984896 etc.. etc...etc