1. Well paced and informative. I bought a book that talked about this spiral and tried to do it but the book didnt actually tell me how to figure out the dimensions.
    Excellent. Thank you.

  2. Interesting Sherrie, I just gave my talk on Islam, Mathematics, and Culture to the Masonic Lodge where I live. I've never been in their building before. It was very enjoyable and they were a very accommodating group. I like your youtube channel.

  3. you are supposed to use a compass when you drop it down.
    you would put one side of the compass to the mid point on one of the sides and the other side of the compass to the corner of the square.
    follow the diagonal line.

  4. You neglect one very important step to the understanding of this process…the divided square base…the diagonal you create….this end point on the base is anchored…fixed…to assist to create the arc…the other point of the angle line …is the end of the line…which forms the arc…in case anyone was wondering how the heck he got this arc and from what…Important step to the understanding and construction..

  5. Oh O get it, why didn't the guy just say it. I mean he's taking the time to make this and he's leaving out obvious stuff. And why does he say drop it down. What kind of mathematical term is this? Geeze

  6. Drop it down? You need to explain that this is done with a compass and has to be precise in order to represent the golden ratio. This is a critical step that you are leaving out. This will leave students confused and misinformed.

  7. Thanks for your explainations, very clear. Did you see Nature by numbers video? I have a question about the hexagons if you don't mind I will ask. thanks

  8. @andymillerisdabest Im not sure why he left this out on the video but: If you have a compass place the point on the middle of the bottom of the square ( where its divided) lengthen the compass so it aligns to the top of the corner of the square( where he begins to draw) and swing the arc down. He should hand draw it since its not accurate. hope this is helpful

  9. You have no idea how excited this made me! Math is so awesome! Man, I missed it.
    Great set of videos you've got here.

  10. @TwoDigitz | I understand what he's doing but I have no idea why he didn't just use a compass or a string or something to show that it was a circle.

  11. The arc has the radius of the square root of 5, that's why the diagonal from the midpoint of the square to the vertex of the square is equal to the side of the same midpoint to the adjacent corner of the golden rectangle. He basically makes the arc by drawing a section of a circle of radius square root of 5. This is why the length of the initial golden rectangle is 1 + sqrt(5), because the sqrt(5) is the radius of the circle and 1 is half the length of the square.

  12. But how are we supposed to know how big to make the arch? This driving me crazy. I drew it equal (another '1' in this case), when I realized that didn't work as I continued I tried free handing it a few times. Nothing I do adds up later on. They either all started turning into squares or the rectangle weren't the size they should be when I continued the process(es) within the original "golden rectangle". Just…what the hell?

  13. To those who don't get the arc part: get a compass, fix it on the start of the diagonal line, put the pencil on the end of the diagonal and drop it down clockwise.

  14. If you forget the actual formula for the golden ratio, an easy way to approximate it: start w a "fraction" w 2 as the numerator & 1 as the denominator (2/1=2). Sum the numerator & denominator to get your new numerator & use the old numerator as your new denominator ((2+1)/2=1.5). Keep repeating this method (5/3=1.6, 8/5=1.625…), & you get closer & closer to the golden ratio. At 6765/4181, you get the same value that you get for the golden ratio as displayed on a standard calculator: 1.6180339.

  15. When he says "drop it down" he means that the distance from half way along the bottom side of the square to a corner on the opposite side equals the distance from half way along the bottom of the square to the bottom corner of a golden rectangle projected from it.

    When he makes the arc from the top of the square to the bottom of the rectangle, he illustrates PI's role in projecting a golden rectangle. Interesting because the presence of PI is not clear In the formula for PHI ((1+√5)/2)

  16. because the arch is formed by sweeping out the diagonal line (of length square root 5). think of a clock hand. The distance from the center of the clock to 12 o'clock is the same as the distance from the center of the clock to 3 o'clok. done

  17. Origami pyramid windmill propeller skies search engine optimization company and harvest moon landing pages. Origami golden rectangle with friends and family reunion mythical creatures who hubbub about this.

  18. Thank you so much for this. Found this very helpful and intriguing. I did have one question. How do you know at what length and how far you should draw that curved line? Or is that not important?

  19. I hear the Golden Ratio is the most irrational number, period. But isn't that surprising that that most irrational number, should be minimal-order algebraic!

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