Strogatz, an applied mathematics professor at Cornell University and author of The Joy of X, has spent his life trying to make others see math the way he does, as a beautiful challenge with real-world implications instead of confusing mumbo jumbo.
We may never completely come around to his side, but it turns out that the math you learned (and hated) back in high school has plenty of surprising real-world implications. Here, the good mathematician offers up a few lessons about math that won't make your head hurt. In fact, they'll boost your life for the better. (And for more great life advice—no calculator required—sign up to receive the FREE Daily Dose newsletter!)
1. Run a Faster 5K
Problem: You can't seem to shave any time off your shorter runs
Math theory: Calculus of variations, Newton's second law
Solution: Conventional wisdom says to save a little energy for a burst of speed at the end of the race, says Strogatz. But mathematicians contend if you have enough energy left for a final spurt of speed, you've failed to reach your optimal velocity—and you're flat-out doing it wrong. The most efficient way to run a race is to think of the race in three parts, according to a study by famous mathematician Joseph B. Keller, Ph.D. During the first few seconds, you should run as fast as possible before leveling off for the second phase. The last few seconds of the race, you should be dragging your butt across the finish line. Basically, if you still have energy left for a final burst of speed, that energy would have been more efficiently used by spreading it out over the duration of the course. (If you're a new runner, read The Weekend Warrior's 5K Plan to cross the finish line strong in just 6 weeks.)
2. Apply Discounts at the Cash Register
Problem: You can't figure out if your should apply the discount before or after tax
Math theory: Commutative law
Solution: It actually doesn't matter, Strogatz says. While you're wracking your brain about the 20-percent-off coupon, you could be high-tailing it out of the store if you'd been paying attention back in the ninth grade. Say the pants you're looking at are $50 with an 8 percent sales tax. The clerk says she'll take 20 percent off after tax, so you get more money back. You counter, asking to take the 20 percent off before, so you pay less in sales tax. So who's wrong? No one. Your way: $50 minus 20 percent reduces the price to $40, multiplied by 8-percent tax for a final price of $43.20. Her way: $50 plus 8-percent tax is $54 minus the 20 percent. That final price? $43.20. In both situations, you're simply switching the order of multiplication, not the numbers themselves. Because of commutative law, it works out the same.
3. Get More Cream Cheese on Your Bagel (Seriously)
Problem: You can't spread enough stuff on your breakfast bagel
Math theory: Mobias strip
Solution: Turns out, you've been putting cream cheese on your bagel the wrong way all along. Think of a Mobias strip as a buckled belt with a single half-twist in it, Strogatz says. It's unique because it's a shape with one continuous surface—essentially the inside is connected to the outside, and vice-versa. George Hart, Ph.D, geometric sculptor and bagel math extraordinaire, found by cutting the bagel into a variation on a Mobias strip—essentially creating two interlocking links—you create more surface area, and thus more room for a delicious spread. For exact instructions, check out this video of Hart explaining it. Despite the bagel's odd geometric shape, you can even toast it.
4. Keep a Tennis Ball in Bounds
Problem: You keep hitting tennis balls out of bounds
Math theory: Vector calculus
Solution: Factor in the vectors. Say you're playing tennis with the boss and the ball is hurtling toward the boundary line, so you take one desperate whack in an attempt to impress the big guy with a running forehand down the inside of the line. But despite your solid hit, the ball bounces out of bounds. That's because you failed to think about the vectors. When you hit the ball, you didn't factor the force your body's velocity would impart on the ball—in addition to the force of the racket. Your new move: Aim the ball across the court in order to compensate. (Want more tips for being the next Roger Federer? Learn 7 Fixes to Help You Play Tennis Like a Pro.)
5. Meet Your Other Half
Problem: You don't know when to settle down with the right girl
Math Theory: e, optimal stopping theory
Solution: You can figure out when you'll meet Mrs. Right by using e (2.71828), an advanced calculus integral that allows you to solve problems involving a lot of randomness and choices, Strogatz says. This requires a little guess work, but, hey, nothing's perfect. Math can't solve all of your problems, after all.
It goes like this: Assume all the women you date would marry you if you asked, and there are no second chances. First, figure out what you consider your "prime" dating years—between ages 20 and 35. Step one: Divide your prime dating years into two sections. Spend the first 7.5 years dating around, establishing what you like and don't like in potential partners. When you hit 7.5 years, assess the women you've dated so far and establish who you felt was the closest to being "the one." She—for lack of a better term—is your #2 dream girl. Then, start to date in a more serious manner. As soon as you find someone who you like more than #2 dream girl, congrats—you've found your soul mate! The logic is that since you've already met your #2 girl, anyone better must be #1—and no one is better than #1. Just hope she isn't also using this logic if you meet her in the first half.
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