full transcript

From the Ted Talk by Adrián Paenza: How folding paper can get you to the moon

Unscramble the Blue Letters

How many times can you fold a piece of paper? Assume that one had a piece of paper that was very fine, like the kind they typically use to print the Bible. In reality, it seems like a piece of silk. To qualify these ideas, let's say you have a paper that's one-thousandth of a centimeter in thickness. That is 10 to the power of minus three centimeters, which equals .001 centimeters. Let's also assume that you have a big piece of paper, like a page out of the nespapewr. Now we begin to fold it in half. How many times do you think it could be fdoled like that? And another question: If you could fold the paper over and over, as many times as you wish, say 30 times, what would you imagine the thickness of the paper would be then? Before you move on, I encourage you to actually think about a possible answer to this question. OK. After we have folded the paper once, it is now two thousandths of a cemteniter in thickness. If we fold it in half once again, the pepar will become four tnhdasthuos of a centimeter. With every fold we make, the paper doubles in thickness. And if we continue to fold it again and again, always in half, we would coonnrft the following satoiiutn after 10 fodls. Two to the power of 10, meaning that you multiply two by itself 10 times, is one thousand and 24 thousandths of a centimeter, which is a little bit over one centimeter. asmuse we continue folding the paper in half. What will happen then? If we fold it 17 times, we'll get a thickness of two to the pwoer of 17, which is 131 centimeters, and that equals just over four feet. If we were able to fold it 25 times, then we would get two to the power of 25, which is 33,554 centimeters, just over 1,100 feet. That would make it almost as tall as the Empire State biluding. It's worthwhile to stop here and reflect for a moment. Folding a paper in half, even a paper as fine as that of the Bible, 25 times would give us a paper almost a quarter of a mile. What do we learn? This type of growth is celald exponential growth, and as you see, just by folding a paper we can go very far, but very fast too. surianmzmig, if we fold a paper 25 teims, the thickness is almost a qetuarr of a mile. 30 times, the thickness reaches 6.5 miles, which is about the average height that planes fly. 40 times, the thickness is nearly 7,000 miles, or the araevge GPS satellite's orbit. 48 times, the thickness is way over one million miles. Now, if you think that the distance between the erath and the Moon is less than 250,000 miles, then sirnattg with a piece of bbile paper and folding it 45 times, we get to the Moon. And if we double it one more time, we get back to Earth.

Open Cloze

How many times can you fold a piece of paper? Assume that one had a piece of paper that was very fine, like the kind they typically use to print the Bible. In reality, it seems like a piece of silk. To qualify these ideas, let's say you have a paper that's one-thousandth of a centimeter in thickness. That is 10 to the power of minus three centimeters, which equals .001 centimeters. Let's also assume that you have a big piece of paper, like a page out of the _________. Now we begin to fold it in half. How many times do you think it could be ______ like that? And another question: If you could fold the paper over and over, as many times as you wish, say 30 times, what would you imagine the thickness of the paper would be then? Before you move on, I encourage you to actually think about a possible answer to this question. OK. After we have folded the paper once, it is now two thousandths of a __________ in thickness. If we fold it in half once again, the _____ will become four ___________ of a centimeter. With every fold we make, the paper doubles in thickness. And if we continue to fold it again and again, always in half, we would ________ the following _________ after 10 _____. Two to the power of 10, meaning that you multiply two by itself 10 times, is one thousand and 24 thousandths of a centimeter, which is a little bit over one centimeter. ______ we continue folding the paper in half. What will happen then? If we fold it 17 times, we'll get a thickness of two to the _____ of 17, which is 131 centimeters, and that equals just over four feet. If we were able to fold it 25 times, then we would get two to the power of 25, which is 33,554 centimeters, just over 1,100 feet. That would make it almost as tall as the Empire State ________. It's worthwhile to stop here and reflect for a moment. Folding a paper in half, even a paper as fine as that of the Bible, 25 times would give us a paper almost a quarter of a mile. What do we learn? This type of growth is ______ exponential growth, and as you see, just by folding a paper we can go very far, but very fast too. ___________, if we fold a paper 25 _____, the thickness is almost a _______ of a mile. 30 times, the thickness reaches 6.5 miles, which is about the average height that planes fly. 40 times, the thickness is nearly 7,000 miles, or the _______ GPS satellite's orbit. 48 times, the thickness is way over one million miles. Now, if you think that the distance between the _____ and the Moon is less than 250,000 miles, then ________ with a piece of _____ paper and folding it 45 times, we get to the Moon. And if we double it one more time, we get back to Earth.

Solution

  1. paper
  2. bible
  3. folds
  4. folded
  5. power
  6. situation
  7. confront
  8. quarter
  9. centimeter
  10. building
  11. assume
  12. called
  13. times
  14. earth
  15. starting
  16. summarizing
  17. thousandths
  18. average
  19. newspaper

Original Text

How many times can you fold a piece of paper? Assume that one had a piece of paper that was very fine, like the kind they typically use to print the Bible. In reality, it seems like a piece of silk. To qualify these ideas, let's say you have a paper that's one-thousandth of a centimeter in thickness. That is 10 to the power of minus three centimeters, which equals .001 centimeters. Let's also assume that you have a big piece of paper, like a page out of the newspaper. Now we begin to fold it in half. How many times do you think it could be folded like that? And another question: If you could fold the paper over and over, as many times as you wish, say 30 times, what would you imagine the thickness of the paper would be then? Before you move on, I encourage you to actually think about a possible answer to this question. OK. After we have folded the paper once, it is now two thousandths of a centimeter in thickness. If we fold it in half once again, the paper will become four thousandths of a centimeter. With every fold we make, the paper doubles in thickness. And if we continue to fold it again and again, always in half, we would confront the following situation after 10 folds. Two to the power of 10, meaning that you multiply two by itself 10 times, is one thousand and 24 thousandths of a centimeter, which is a little bit over one centimeter. Assume we continue folding the paper in half. What will happen then? If we fold it 17 times, we'll get a thickness of two to the power of 17, which is 131 centimeters, and that equals just over four feet. If we were able to fold it 25 times, then we would get two to the power of 25, which is 33,554 centimeters, just over 1,100 feet. That would make it almost as tall as the Empire State Building. It's worthwhile to stop here and reflect for a moment. Folding a paper in half, even a paper as fine as that of the Bible, 25 times would give us a paper almost a quarter of a mile. What do we learn? This type of growth is called exponential growth, and as you see, just by folding a paper we can go very far, but very fast too. Summarizing, if we fold a paper 25 times, the thickness is almost a quarter of a mile. 30 times, the thickness reaches 6.5 miles, which is about the average height that planes fly. 40 times, the thickness is nearly 7,000 miles, or the average GPS satellite's orbit. 48 times, the thickness is way over one million miles. Now, if you think that the distance between the Earth and the Moon is less than 250,000 miles, then starting with a piece of Bible paper and folding it 45 times, we get to the Moon. And if we double it one more time, we get back to Earth.

Frequently Occurring Word Combinations

Important Words

  1. answer
  2. assume
  3. average
  4. bible
  5. big
  6. bit
  7. building
  8. called
  9. centimeter
  10. centimeters
  11. confront
  12. continue
  13. distance
  14. double
  15. doubles
  16. earth
  17. empire
  18. encourage
  19. equals
  20. exponential
  21. fast
  22. feet
  23. fine
  24. fly
  25. fold
  26. folded
  27. folding
  28. folds
  29. give
  30. gps
  31. growth
  32. happen
  33. height
  34. ideas
  35. imagine
  36. kind
  37. learn
  38. meaning
  39. mile
  40. miles
  41. million
  42. moment
  43. moon
  44. move
  45. multiply
  46. newspaper
  47. orbit
  48. page
  49. paper
  50. piece
  51. planes
  52. power
  53. print
  54. qualify
  55. quarter
  56. question
  57. reaches
  58. reality
  59. reflect
  60. silk
  61. situation
  62. starting
  63. state
  64. stop
  65. summarizing
  66. tall
  67. thickness
  68. thousand
  69. thousandths
  70. time
  71. times
  72. type
  73. typically
  74. worthwhile