# Math Horizons September 2014 : Page 29

## DO THE MATH!

### Andrea Hawksley

<br /> Fibonacci Lemonade<br /> <br /> How would one make mathematical cuisine? Not just food that looks mathematical (like fractal cookies), but something that you must eat and taste in order to experience its mathematical nature.<br /> <br /> The answer I came up with is simple enough that anyone can make it at home. It is surprisingly beautiful and delicious . . . layered drinks!<br /> <br /> These aren’t just any layered drinks, of course. In our layered lemonade, the proportions of sugar (simple syrup) and lemon juice in each layer are determined by the Fibonacci sequence. The intensity of flavors increases exponentially as you drink it. The sweeter layers are denser and naturally stay lower. Indeed, all layered drinks have the intrinsic mathematical property that they are monotonically increasing in sweetness.<br /> <br /> Additionally, the ratio of sugar to lemon juice in our lemonade isn’t constant. The top two layers of our drink have one part simple syrup, while the second and third layers have one part lemon juice. Following the Fibonacci rule, each subsequent layer has proportions that are the sum of the proportions in the two previous layers. Table 1 shows the proportions of our six-layer drink.<br /> <br /> So as the drink is consumed, the ratio of sugar to lemon juice approaches the golden ratio. This drink may be the world’s first tastable example of the relationship between the Fibonacci sequence and the golden ratio!<br /> <br /> Surprisingly, using golden ratio relative proportions of lemon juice and simple syrup makes rather good lemonade. When consumed, the beverage starts out fairly flavorless, then rapidly ramps up. It also alternates between being a bit sweet to being a bit sour as the approximation of the golden ratio alternates between being slightly high and slightly low.<br /> <br /> You too can make Fibonacci lemonade and experience the taste of exponential flavor, the golden ratio, and the Fibonacci sequence. Just follow the recipe at left!<br /> <br /> The Method<br /> <br /> Fill four glasses with ice. Then, do the following steps for each layer. Note: You must start with the sweetest layer—the sixth layer in my example—and work your way upward.<br /> <br /> 1. Add the amount of lemon juice and simple syrup given in table 1 to your liquid measuring cup.<br /> <br /> 2. Add food coloring if desired.<br /> <br /> 3. Fill the measuring cup to the 1/2 cup line with water.<br /> <br /> 4. Stir well.<br /> <br /> 5. Pour the mixture into your glasses. You should pour slowly and directly onto an ice cube. This will help keep the layers distinct. (For a less watered-down experience, make the drinks without ice. This is much more difficult—you must use a spoon to keep the layers from mixing.)<br /> <br /> Finally, sip your mathematical masterpiece.<br /> <br /> Andrea Hawksley is a software developer and mathematical artist. She is a cofounder of the Octahedral Group for math artists and works on virtual reality video with eleVR. Email: hawksley@gmail.com

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