In this video I go over another example on determining the arc length of a parametric curve and this time determine the length of one arch of a the famous cycloid shape. In the derivation I use the arc length formula for parametric curves as well as the Pythagorean and Half-Angle Trigonometric Identities. The resulting value is that the arch length of one arch is 8 times the radius of the circle that generates the cycloid! This is quite a fascinating result, and so I have also included a brief history lesson on this finding as well. The length of a cycloid was first found by the English Architect Sir Christopher Wren in 1658. Wren’s method of determining the cycloid length was much more tedious than our more advanced calculus version, in which his method required the dissection of the cycloid into segments of a circle. Along with Wren, I also go over a brief history lesson on the famous St. Paul’s Cathedral, in which Wren was the designer and architect, and bring up the very interesting point that it looks oddly like the United States White House. This similarity is something that I may look further into in the near future… This is a great video in deriving the length of a cycloid, as well as some of the history behind it, so make sure to watch this video!
Watch on VidMe: https://vid.me/UeOhf
Watch on BitChute: https://www.bitchute.com/video/W2U9K4jz0msh/
Download PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIhuUD_0I90V0MNJvymg
View Video Notes Below!
Download These Notes: Link is in Video Description.
View These Notes as an Article: https://steemit.com/@mes
Subscribe via Email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donate
Reuse of My Videos:
- Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.
Fight Back Against Censorship:
- Bookmark sites/channels/accounts and check periodically
- Remember to always archive website pages in case they get deleted/changed.
Check out my Reddit and Voat Math Forums:
Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
Follow My #FreeEnergy Video Series: https://mes.fm/freeenergy-playlist
USEFUL TIP: If I'm going too fast or too slow, play this video at a different speed.
-- TOP SECRET LIFE HACK: Your brain gets used to faster speed (#Try2xSpeed)
Example: Find the length of one arch of the cycloid x = r(θ - sinθ), y = r(1 - cosθ).
The result of this example says that the length of one arch of a cycloid is eight times the radius of the generating circle.
Brief History Lesson
This was first proved in 1658 by Sir Christopher Wren, who later became the architect of St. Paul's Cathedral in London, England.
https://en.wikipedia.org/wiki/Christopher_Wren
Retrieved: 10 February 2017
Christopher Wren
Reveal spoiler
Sir Christopher Wren PRS (/ˈrɛn/;[2] 30 October 1632 [O.S. 20 October] – 8 March 1723 [O.S. 25 February]) is one of the most highly acclaimed English architects in history.[3] He was accorded responsibility for rebuilding 52 churches in the City of London after the Great Fire in 1666, including what is regarded as his masterpiece, St. Paul's Cathedral, on Ludgate Hill, completed in 1710.
Educated in Latin and Aristotelian physics at the University of Oxford, Wren was a notable anatomist, astronomer, geometer, and mathematician-physicist, as well as an architect. He was a founder of the Royal Society (president 1680–82), and his scientific work was highly regarded by Isaac Newton and Blaise Pascal.
Wren was knighted 14 November 1673. This honour was bestowed on him after his resignation from the Savilian chair in Oxford, by which time he had already begun to make his mark as an architect, both in services to the Crown and in playing an important part in rebuilding London after the Great Fire.[citation needed]
Also his contribution to mathematics should be noted; in 1658, he found the length of an arc of the cycloid using an exhaustion proof based on dissections to reduce the problem to summing segments of chords of a circle which are in geometric progression.
https://en.wikipedia.org/wiki/St_Paul%27s_Cathedral
Retrieved: 10 February 2017
St Paul's Cathedral
Reveal spoiler
St Paul's Cathedral, London, is an Anglican cathedral, the seat of the Bishop of London and the mother church of the Diocese of London. It sits on Ludgate Hill at the highest point of the City of London and is a Grade 1 listed building. Its dedication to Paul the Apostle dates back to the original church on this site, founded in AD 604.[1] The present church, dating from the late 17th century, was designed in the English Baroque style by Sir Christopher Wren. Its construction, completed in Wren's lifetime, was part of a major rebuilding programme in the City after the Great Fire of London.[2]
https://en.wikipedia.org/wiki/Cathedral
Retrieved: 10 February 2017
Cathedral
A cathedral (French: cathédrale from Latin: cathedra, "seat" from the Greek kathédra (καθέδρα), seat, bench, from kata "down" + hedra seat, base, chair) is a Christian church which contains the seat of a bishop,[1] thus serving as the central church of a diocese, conference, or episcopate.[2]
…
Churches with the function of "cathedral" are usually specific to those Christian denominations with an episcopal hierarchy, such as the Roman Catholic, Anglican, Orthodox, and some Lutheran and Methodist churches.[2]
Congratulations @mes, this post is the third most rewarded post (based on pending payouts) in the last 12 hours written by a User account holder (accounts that hold between 0.1 and 1.0 Mega Vests). The total number of posts by User account holders during this period was 1029 and the total pending payments to posts in this category was $1449.01. To see the full list of highest paid posts across all accounts categories, click here.
If you do not wish to receive these messages in future, please reply stop to this comment.