1 00:00:00,000 --> 00:00:06,920 What is surveying? 2 00:00:06,920 --> 00:00:10,480 How do surveyors use geometry? 3 00:00:10,480 --> 00:00:14,600 Surveying is the measurement of angles and distances, elevation, and direction. 4 00:00:14,600 --> 00:00:19,680 It's especially useful for locating property boundaries, construction layout, and map making. 5 00:00:19,680 --> 00:00:24,480 Okay, Terry, can you tell me how surveyors use this equipment and geometry to survey 6 00:00:24,480 --> 00:00:25,480 land? 7 00:00:25,480 --> 00:00:26,480 Yes. 8 00:00:26,480 --> 00:00:27,480 Let's look at this transit. 9 00:00:27,480 --> 00:00:33,000 This is a telescope, a compass, and a protractor, and it's used to measure horizontal and vertical 10 00:00:33,000 --> 00:00:34,400 angles. 11 00:00:34,400 --> 00:00:38,160 You can measure angles in the field with this and measure those same angles back at your 12 00:00:38,160 --> 00:00:40,540 desk with a protractor. 13 00:00:40,540 --> 00:00:45,320 This instrument is used to lay out objects like football fields, baseball fields, soccer 14 00:00:45,320 --> 00:00:46,320 fields. 15 00:00:46,320 --> 00:00:50,320 Today, let's demonstrate how we use this by laying out this football field. 16 00:00:50,320 --> 00:00:51,320 All right. 17 00:00:51,320 --> 00:00:55,080 First, we pick a starting point and set the transit over the point. 18 00:00:55,080 --> 00:00:57,800 We call this point corner number one. 19 00:00:57,800 --> 00:01:02,420 Then we measure 300 feet to the next corner and call it corner number four. 20 00:01:02,420 --> 00:01:04,920 We mark this corner with a corner marker. 21 00:01:04,920 --> 00:01:10,160 With zero on the scale, we look through the telescope and line up corner number four. 22 00:01:10,160 --> 00:01:14,840 We know that the angle between the sides of a rectangle is 90 degrees, so we turn the 23 00:01:14,840 --> 00:01:20,600 telescope towards corner number two until we can read 90 degrees on the transit circle 24 00:01:20,600 --> 00:01:21,600 or scale. 25 00:01:22,120 --> 00:01:27,480 Now we measure the width of the football field, 150 feet, and mark corner number two. 26 00:01:27,480 --> 00:01:31,680 Next, we move the transit over corner number two. 27 00:01:31,680 --> 00:01:36,840 With zero on the scale, we look through the telescope at corner number one marker. 28 00:01:36,840 --> 00:01:41,600 We turn the telescope towards corner number three until we can read 90 degrees on the 29 00:01:41,600 --> 00:01:42,600 scale. 30 00:01:42,600 --> 00:01:46,280 We measure 300 feet and mark corner number three. 31 00:01:46,280 --> 00:01:49,360 We now have all of the corners marked. 32 00:01:49,360 --> 00:01:54,280 Applying one of the basic rules of geometry, we know that the sum of the interior angles 33 00:01:54,280 --> 00:01:58,120 of a four-sided polygon is 360 degrees. 34 00:01:58,120 --> 00:02:03,000 So our last angle must measure 90 degrees for a correct layout. 35 00:02:03,000 --> 00:02:07,760 The rule for checking the angles of any object is that the sum of the interior angles of 36 00:02:07,760 --> 00:02:13,160 a closed polygon is equal to the number of sides minus two times 180 degrees. 37 00:02:13,160 --> 00:02:18,760 You know, Jennifer, the art and science of surveying have been used for over 3,400 years 38 00:02:18,760 --> 00:02:20,960 to map and measure our world. 39 00:02:20,960 --> 00:02:26,320 Today, scientists at NASA are preparing to measure and map the planets of our solar system. 40 00:02:26,320 --> 00:02:28,400 Hmm, who knows? 41 00:02:28,400 --> 00:02:31,360 Maybe one day one of you will help survey Mars. 42 00:02:31,360 --> 00:02:36,800 Did you know that George Washington was a surveyor before he became president? 43 00:02:36,800 --> 00:02:40,560 Did you know Lewis and Clark used transits on the exploration mission? 44 00:02:40,560 --> 00:02:47,720 To understand angles and circumference, let's look at something we can all relate to, pizza. 45 00:02:47,720 --> 00:02:48,720 Take this slice of pizza. 46 00:02:48,720 --> 00:02:53,320 Can you tell just by looking at it how many slices were in the original pizza and how 47 00:02:53,320 --> 00:02:55,160 big a round it was? 48 00:02:55,160 --> 00:02:56,160 Sure you can. 49 00:02:56,160 --> 00:02:57,840 All it takes is a little geometry. 50 00:02:57,840 --> 00:03:02,160 A pizza usually has eight identical slices, but not all of them. 51 00:03:02,160 --> 00:03:05,680 So let's measure the angle width of this slice. 52 00:03:05,680 --> 00:03:08,120 That's the part you put in your mouth first. 53 00:03:08,120 --> 00:03:13,240 Excuse me, sir, what does this protractor read? 54 00:03:13,240 --> 00:03:16,280 The protractor reads an angle width of 45 degrees. 55 00:03:16,280 --> 00:03:17,280 Right. 56 00:03:17,840 --> 00:03:21,120 Now, what is the measurement of all the other angles touching the center? 57 00:03:21,120 --> 00:03:25,120 They have to be equal or the same measurement, 45 degrees. 58 00:03:25,120 --> 00:03:26,120 Right. 59 00:03:26,120 --> 00:03:31,040 Now, most pizzas are circular and circles measure 360 degrees. 60 00:03:31,040 --> 00:03:38,640 If you divide 360 degrees by 45 degrees, the original pizza had eight slices. 61 00:03:38,640 --> 00:03:42,320 Now, let's figure the circumference of this pizza. 62 00:03:42,320 --> 00:03:44,160 Most pizzas are measured in inches. 63 00:03:44,160 --> 00:03:49,080 So, using the pizza with eight slices, if the length of the crust arc is five and a 64 00:03:49,080 --> 00:03:51,400 half inches, how round is your pizza? 65 00:03:51,400 --> 00:04:00,160 If there are eight slices and the crust arc measures 5.5 inches long, then eight times 66 00:04:00,160 --> 00:04:03,880 5.5 inches equals 44 inches. 67 00:04:03,880 --> 00:04:07,600 The pizza has a circumference of 44 inches. 68 00:04:07,600 --> 00:04:08,640 Great. 69 00:04:08,640 --> 00:04:09,640 Try this one. 70 00:04:09,640 --> 00:04:15,280 What if the angle width of your pizza slice measures 30 degrees and the crust arc is two 71 00:04:15,280 --> 00:04:16,840 and a half inches? 72 00:04:16,840 --> 00:04:21,640 How many slices would there be in the original pizza and what is the circumference? 73 00:04:21,640 --> 00:04:23,120 I've got it. 74 00:04:23,120 --> 00:04:27,520 360 degrees divided by 30 degrees equals 12 slices. 75 00:04:27,520 --> 00:04:33,480 12 slices times 2.5 inches equals a circumference of 30 inches. 76 00:04:33,480 --> 00:04:38,920 So, sir, would you rather eat a 12-slice pizza or an eight-slice pizza? 77 00:04:39,520 --> 00:04:40,760 I'll choose the eight slices. 78 00:04:40,760 --> 00:04:42,320 I couldn't possibly eat 12.