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# Stairway

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### Stairway

1. 1. Stairway to Heaven<br />A mathematical exploration<br />
2. 2. There's a lady who's sure all that glitters is goldAnd she's buying a stairway to heaven(And) when she gets there she knows if the stores are all closedWith a word she can get what she came for<br />
3. 3. How long would it take to climb the stairway to heaven?<br />
4. 4. What information do we need to find the answer?<br />
5. 5. Questions<br />Where does heaven begin?<br />How are stairs constructed?<br />How fast does the average person climb stairs?<br />What about using an escalator?<br />
6. 6. Where does heaven begin?<br />Q. Where does Space begin? — Merl H. <br />A. It starts at an altitude of 100 kilometers. People sometimes speak of 50 miles or 60 miles or 62 miles. The most widely accepted altitude where Space begins is 100 kilometers, which is about 62 miles. The U.S. space agency awards astronaut status to persons who fly above 50 miles altitude. <br />
7. 7. Where does heaven begin?<br /> For reference, note that a typical passenger jet cruises at an average altitude of about 30,000 feet which is just under six miles above Earth's surface. The most powerful military jets can't climb much above 100,000 feet, which would be just under 19 miles altitude.  <br />
8. 8. How are stairs constructed?<br />Calculating Rise and Run<br />The first step in building stairs is finding the total rise or overall vertical height the stairs have to cover. Let's say the total rise is 57 in. The next job is to find the rise of each step. Divide 57 by 7 in. (the typical rise per step) to get 8.14. Round down to get the steps: eight. To then determine the actual rise, divide the 57 in. by the eight steps to get 7 1/8 in. per step. <br />
9. 9. How are stairs constructed?<br />You can use that information to find the total run of the staircase--or how much horizontal distance it will cover as it climbs. Multiply the number of steps by the run, or horizontal depth, of each step. The optimum run of each step is no less than 10 in. In our example, the staircase has eight steps, so the total run is 80 in. <br />
10. 10. How fast does the average person climb stairs?<br />Answer: 1 step per second<br />
11. 11. Answer<br />Using 100 km as the distance to heaven, it would take 562,429 steps to build the stairway to heaven.<br />At 1 step per second this means that it would take 156.2 hours or over 6 ½ days!<br />
12. 12. Escalator??<br />A single-width escalator traveling at about 1.5 feet (0.46 m) per second can move an estimated 170 persons per five-minute period.<br />The distance the escalator would travel is 81,714 feet or almost 15 ½ miles.<br />
13. 13. Escalator to Heaven<br />This would take 54476 seconds or 15 hours 7 minutes 56 seconds to ride the Escalator to heaven!!<br />
14. 14. Additional Information<br />The total horizontal run of the Stairway to Heaven would be 88.77 miles or over 3 marathons!<br />The slope of the stairway is 7/10 which is an angle of 35°<br />
15. 15. Information on the Song<br />"Stairway to Heaven" continues to top radio lists of the greatest rock songs, as well as topping a 2006 Guitar World readers poll of greatest guitar solos.<br />
16. 16. Information on the Song<br />On the 20th anniversary of the original release of the song, it was announced via U.S. radio sources that the song had logged up an estimated 2,874,000 radio plays - back to back, that would run for 44 years![6]<br />
17. 17. References<br />Mathalicious – 51 foot ladderhttp://www.mathalicious.com/lesson/51-foot-ladder/<br />Space Today http://www.spacetoday.org/Questions/WhereIsSpace.html<br />Wikipedia – Stairway to Heavenhttp://en.wikipedia.org/wiki/Stairway_to_heaven<br />
18. 18. References<br />Climbing stairs - Yahoo Answers http://answers.yahoo.com/question/index?qid=1006042707287<br />Building a Stairway – Popular Mechanicshttp://www.popularmechanics.com/home/how-to-plans/woodworking/4224738<br />Escalators – Wikipediahttp://en.wikipedia.org/wiki/Escalator<br />