WEBVTT 00:00:02.220 --> 00:00:09.779 Hi, what is it that draws you in? If you see 00:00:09.779 --> 00:00:13.419 a beautiful flower, do you stop and take a second 00:00:13.419 --> 00:00:17.420 look? Do you notice the colors that are stretching 00:00:17.420 --> 00:00:22.679 across the sky at sunset? Does the face of a 00:00:22.679 --> 00:00:28.219 newborn baby capture your attention? All three 00:00:28.219 --> 00:00:32.619 of these draw me into a different world. For 00:00:32.619 --> 00:00:36.159 a moment, I stop thinking about what I need to 00:00:36.159 --> 00:00:42.280 do next. I find myself enjoying the beauty, reflecting, 00:00:42.439 --> 00:00:47.140 and sometimes even wondering. Now, you may find 00:00:47.140 --> 00:00:50.960 this odd, but shapes can do something similar 00:00:50.960 --> 00:00:54.920 for me. Sometimes it is a simple design on a 00:00:54.920 --> 00:00:58.780 t -shirt or a particular creative logo. Other 00:00:58.780 --> 00:01:01.890 times it is a repeating pattern on a floor. or 00:01:01.890 --> 00:01:06.849 a wall, or a building. I am drawn to shapes, 00:01:07.030 --> 00:01:10.870 especially shapes that are filled with an interesting 00:01:10.870 --> 00:01:16.569 pattern. Mathematician Paul Lockhart writes something 00:01:16.569 --> 00:01:22.890 simple, yet profoundly simple. Paul says, every 00:01:22.890 --> 00:01:28.390 equation has a shape. Think about that for a 00:01:28.390 --> 00:01:31.670 moment. When we first encounter an equation, 00:01:31.969 --> 00:01:36.209 we usually see a collection of letters, numbers, 00:01:36.430 --> 00:01:41.670 and symbols. Consider the equation y equals x 00:01:41.670 --> 00:01:47.510 squared. Now, on the page, it may not look particularly 00:01:47.510 --> 00:01:52.549 inspiring. It is simply a rule. Choose a value 00:01:52.549 --> 00:01:56.010 for x, square it, and that gives you the corresponding 00:01:56.010 --> 00:02:00.549 value of y. place those points on a coordinate 00:02:00.549 --> 00:02:03.769 plane, and something quite different happens. 00:02:04.329 --> 00:02:09.509 The equation becomes a parabola. What looked 00:02:09.509 --> 00:02:13.449 like a short line of mathematical notation opens 00:02:13.449 --> 00:02:18.069 into a smooth symmetrical curve. The equation 00:02:18.069 --> 00:02:24.490 has been given a visible shape. Okay, now change 00:02:24.490 --> 00:02:29.550 the equation slightly to y equals minus. x squared. 00:02:30.509 --> 00:02:34.370 Adding one small negative sign turns the entire 00:02:34.370 --> 00:02:40.909 parabola upside down. Or consider this equation, 00:02:41.250 --> 00:02:47.270 x squared plus y squared equals one. Now, it 00:02:47.270 --> 00:02:49.689 may initially appear to be a strange collection 00:02:49.689 --> 00:02:53.449 of squares and numbers, but when we graph it, 00:02:53.569 --> 00:02:59.969 a circle emerges. Isn't it ironic that a circle 00:02:59.969 --> 00:03:03.949 is somehow contained with the equation of squared 00:03:03.949 --> 00:03:07.810 values? And of course, the graph did not create 00:03:07.810 --> 00:03:11.729 it. The graph allowed us to see what had been 00:03:11.729 --> 00:03:16.689 there all along. One of the things I love about 00:03:16.689 --> 00:03:20.650 mathematics is that algebra and geometry seem 00:03:20.650 --> 00:03:23.650 like two completely different worlds. Algebra 00:03:23.650 --> 00:03:27.379 speaks through symbols and equations. Geometry 00:03:27.379 --> 00:03:32.080 speaks through lines, curves, distances, and 00:03:32.080 --> 00:03:38.759 shapes. But a graph allows those two worlds to 00:03:38.759 --> 00:03:43.620 meet. The equation tells us how the numbers are 00:03:43.620 --> 00:03:48.039 related. The shape lets us see that relationship 00:03:48.039 --> 00:03:54.139 all at once. And perhaps that is why shapes draw 00:03:54.139 --> 00:03:58.870 us in. We are not merely looking at individual 00:03:58.870 --> 00:04:05.169 points or lines or even colors. Our minds gather 00:04:05.169 --> 00:04:09.009 those separate details and recognize a larger 00:04:09.009 --> 00:04:13.110 pattern. And through that pattern, we begin to 00:04:13.110 --> 00:04:18.250 see meaning. Mathematics reminds us that reality 00:04:18.250 --> 00:04:22.670 can contain more than what is immediately visible. 00:04:23.720 --> 00:04:27.420 Sometimes a relationship is present long before 00:04:27.420 --> 00:04:31.560 we have found the right way to see it. An equation 00:04:31.560 --> 00:04:35.199 can remain nothing more than symbols on a page. 00:04:35.920 --> 00:04:41.779 That happens many times for me. But math is at 00:04:41.779 --> 00:04:46.720 its best is when it becomes a doorway into an 00:04:46.720 --> 00:04:52.100 entirely different world. And perhaps the same 00:04:52.100 --> 00:04:56.160 is true elsewhere in life. So, as we begin this 00:04:56.160 --> 00:05:00.540 week, consider these questions. What might already 00:05:00.540 --> 00:05:04.339 be present in your life, waiting for you to discover 00:05:04.339 --> 00:05:08.819 a new way of seeing it? Perhaps it is a close 00:05:08.819 --> 00:05:12.180 friend or family member whose presence has become 00:05:12.180 --> 00:05:15.759 so familiar that you sometimes take it for granted. 00:05:16.480 --> 00:05:20.180 And seeing that person every day can be a little 00:05:20.180 --> 00:05:24.160 like looking at an equation. The meaning is there, 00:05:24.360 --> 00:05:27.680 but we may no longer recognize the beautiful 00:05:27.680 --> 00:05:32.699 shape it has created. Who has helped shape your 00:05:32.699 --> 00:05:36.740 life for the better? And perhaps today is the 00:05:36.740 --> 00:05:40.920 day to see that person differently and to let 00:05:40.920 --> 00:05:45.240 them know how much their life has shaped yours.