1 00:00:00,000 --> 00:00:05,000 Hi, we're from Fairview Maths Academy, Dane, Ohio. 2 00:00:05,000 --> 00:00:07,000 We're SEMA students. 3 00:00:07,000 --> 00:00:12,000 Hi, we're from Roosevelt Middle School in Springfield, Ohio. 4 00:00:12,000 --> 00:00:14,000 We're SEMA students. 5 00:00:14,000 --> 00:00:17,000 NASA Connect asked us to help you learn this lesson. 6 00:00:17,000 --> 00:00:20,000 There are many ways to divide the class up 7 00:00:20,000 --> 00:00:24,000 to check for the Fibonacci ratio in the objects you've collected, 8 00:00:24,000 --> 00:00:27,000 but we've decided to have three groups. 9 00:00:27,000 --> 00:00:30,000 The first group will measure natural objects. 10 00:00:30,000 --> 00:00:33,000 First, count the number of sides of the unpeeled banana. 11 00:00:33,000 --> 00:00:36,000 Write this number on the worksheet. 12 00:00:36,000 --> 00:00:41,000 On the pineapple, count the number of squares in two adjacent spirals. 13 00:00:41,000 --> 00:00:45,000 Are the adjacent numbers in the Fibonacci sequence? 14 00:00:45,000 --> 00:00:48,000 Count the segments of the halved grapefruit. 15 00:00:48,000 --> 00:00:50,000 Is the grapefruit golden? 16 00:00:50,000 --> 00:00:54,000 Examine the pine cone for the number of spirals that go to the right 17 00:00:54,000 --> 00:00:59,000 and compare that number to the number of spirals that go to the left. 18 00:00:59,000 --> 00:01:01,000 Look at the daisy. 19 00:01:01,000 --> 00:01:05,000 Compare the number of petals that grow in a clockwise direction 20 00:01:05,000 --> 00:01:09,000 to the number that grow in a counterclockwise direction. 21 00:01:09,000 --> 00:01:11,000 Is your daisy golden? 22 00:01:11,000 --> 00:01:16,000 Now check any other natural objects that you have brought to class. 23 00:01:16,000 --> 00:01:22,000 The second group uses body measurements that approximate the golden ratio. 24 00:01:22,000 --> 00:01:28,000 Write the ratio of finger segments in one finger to the number of fingers on one hand. 25 00:01:28,000 --> 00:01:30,000 Is your hand golden? 26 00:01:30,000 --> 00:01:34,000 Now measure each student's height and record the results on the worksheet. 27 00:01:34,000 --> 00:01:37,000 Measure each student from the top of their head 28 00:01:37,000 --> 00:01:40,000 to the top of the middle finger of the outstretched arm. 29 00:01:40,000 --> 00:01:42,000 Record the results. 30 00:01:42,000 --> 00:01:45,000 What is the ratio of the height to the measure of the length 31 00:01:45,000 --> 00:01:48,000 from the top of the head to the end of the outstretched arm? 32 00:01:48,000 --> 00:01:51,000 Does it approximate the golden ratio? 33 00:01:51,000 --> 00:01:56,000 Measure the height of each student and the navel to floor height of each. 34 00:01:56,000 --> 00:02:01,000 Write the result as a ratio of body height to navel to floor height. 35 00:02:01,000 --> 00:02:04,000 Is the result close to the golden ratio? 36 00:02:04,000 --> 00:02:08,000 Measure each student's arm length and fingertip to the elbow. 37 00:02:08,000 --> 00:02:10,000 Write the result as a ratio. 38 00:02:10,000 --> 00:02:12,000 Is it golden? 39 00:02:12,000 --> 00:02:15,000 Group 3 measures man-made objects. 40 00:02:15,000 --> 00:02:21,000 Verify the Fibonacci numbers by measuring the length and width of an index card. 41 00:02:21,000 --> 00:02:23,000 Try this with an ID card. 42 00:02:23,000 --> 00:02:27,000 Measure other objects in the classroom or brought to class. 43 00:02:27,000 --> 00:02:30,000 When all groups finish with their explorations, 44 00:02:30,000 --> 00:02:34,000 they could summarize their findings and report to the rest of the class. 45 00:02:34,000 --> 00:02:40,000 Special thanks to our AIAA students from the University of Cincinnati. 46 00:02:40,000 --> 00:02:42,000 Great job, guys! 47 00:02:42,000 --> 00:02:45,000 After you've completed the activity on the golden ratio, 48 00:02:45,000 --> 00:02:50,000 you should analyze your observations and respond to the following. 49 00:02:50,000 --> 00:02:56,000 In four sentences, describe the activity you just completed. 50 00:02:56,000 --> 00:03:01,000 Was everything you examined golden? 51 00:03:01,000 --> 00:03:06,000 How do you determine if an object is golden? 52 00:03:06,000 --> 00:03:09,000 Do you think that there is another special ratio, 53 00:03:09,000 --> 00:03:13,000 like the golden ratio, that exists in nature? 54 00:03:13,000 --> 00:03:15,000 Why? 55 00:03:15,000 --> 00:03:19,000 Teachers, check out our NASA Connect website.