Golden Ratio Construction

I walk through on how to construct the Golden Ratio with just a compass, straight-edge and pencil. I also prove algebraically that the construction works.
Construction Steps:
1) Create segment AB.
2) Bisect segment AB, call midpoint M.
3) Construct a segment perpendicular to segment AB that intersects point B.
4) Copy length of segment AM (also equal to MB) onto the perpendicular segment away from B. Call new point C.
5) Construct segment AC.
6) Copy length of segment AM onto segment AC away from C. Call new point D.
7) Copy length of segment AD onto segment AB away from A. Call new point G.
AB/AG = phi = Golden Ratio

Пікірлер: 27

  • @JohnPretto
    @JohnPretto4 жыл бұрын

    Had a ton of fun watching. Thanks.

  • @MartinLlorensCaminotti
    @MartinLlorensCaminotti6 ай бұрын

    Great video! Very good content, thanks! Maybe if you use graph paper, the accuracy will be easier and higher.

  • @itshardouthere4the5.47
    @itshardouthere4the5.474 жыл бұрын

    👍👍! Love the homemade compas. I made mine as well. 👍

  • @PASHKULI
    @PASHKULI2 жыл бұрын

    that was quite interesting... you made a right triangle with sides 2x and 1x, thus the hypotenuse is x√5 (x is units)... then the 1u got subtracted from x√5 leaving us with (√5 -1)x. So basically you constructed to touching circles one with rA = (√5-1)x and the other with rB = 1x Then we have 2x = rA + rB = (√5-1)x + 1x, thus x = φ! Now... we can have a Golden triangle, which hypotenuse is φ and the other sides are 1 and √φ (directly from the equation: φ = √φ + 1 or φ² = (√φ)² + 1², which is a right triangle by Pythagoras theorem, a Golden one)!

  • @capnchip
    @capnchip5 жыл бұрын

    Very interesting! I suggest you consider a REAL compass!

  • @abhijeetdutta6156
    @abhijeetdutta6156 Жыл бұрын

    Beautiful ❤️

  • @kkrishnanandasingh2816
    @kkrishnanandasingh28166 жыл бұрын

    Thank you...

  • @jimhumphrey
    @jimhumphrey2 жыл бұрын

    I see comments that suggest John needs a better compass. John is a mathematician, not a draftsman, I think that is clear. I have built several wooden shop built compasses that are similar to the one he is using and quite frankly they are as accurate as my professional compass.

  • @johnsaegh9488
    @johnsaegh94887 жыл бұрын

    89 and 144 are Fibonacci numbers. My construction was off by a millimeter.

  • @TibiSitibira

    @TibiSitibira

    6 жыл бұрын

    ( 1 + √5 ) / 2 = Φ and by the way..... it have nothing to do with humans..... it always existing in the universe..... 🌏 📡🌏 👣🕘 💎👽☠☼☾☄ェヽ・ㇺㇾㇽ₪ɨʈɨЬɨʀа₪ヽ・ェㇺㇾㇽ✶☥✨🌛🌄⊀✶⋊🐺🐾☆🐜🐜▲▴◭

  • @B1N4RYGH0ST
    @B1N4RYGH0ST6 жыл бұрын

    Hi, John. Who makes that compass that you are using?

  • @vurimalla

    @vurimalla

    5 жыл бұрын

    dear, you can get on amazon. search and get .... love you.

  • @vurimalla
    @vurimalla5 жыл бұрын

    dear , can you teach me. i am about to start construction my sweet home....can we do sample architechure online.....please let me know....love you !!

  • @holyshit922
    @holyshit9225 жыл бұрын

    144/89 is nice approximation and comes from Fibonacci sequence You were close to this

  • @theignorantphilosopher4855
    @theignorantphilosopher48554 жыл бұрын

    All though I did enjoy watching this, it does seem an incredible convoluted way of doing it, and furthermore I'm not sure I entirely understood your proof. I'm sure I've missed something, but it seems to be that you claim 1+1 to be equal to the square root of 5, which is of course not accurate. Of the top of my head, I'd use much the same process as you, drawing a right angled triangle ABC, where |AB| = 2 and |BC| =1. Form there of course there are multiple avenue. You can extend the hypotenuse by one and bisect, you can subtract 1 from the hypotenuse, bisect and add one, and so on. At any rate, it would see I didn't quite follow, but I think I got the gist of it.

  • @johnsaegh9488
    @johnsaegh94887 жыл бұрын

    @13.40, anecdotally!! not antic-totally =(

  • @stefanbandas2157
    @stefanbandas21572 жыл бұрын

    I enjoyed this construction. Some constructive criticism: If I were your student, I would want more explanation of what you are doing and why. You bisect the line segment, but you never explain that you are envisioning the line segment AB to be 2 units. You don’t explain that you are creating a unit circle with a radius of 1 unit to construct a right triangle with leg lengths of 1 and 2, therefore a hypotenuse of 5^.5, or why 1 unit from the vertex at D is the length your looking to bring to line segment AB. Take it or leave it, overall I enjoyed your presentation, but you spent more talking about the proof and percent error than what you were actually doing.

  • @stewartmcmanus3991
    @stewartmcmanus39913 жыл бұрын

    Not surprising that I found algebra incomprehensible at grammar school.

  • @josephrikers1111
    @josephrikers11112 жыл бұрын

    Agriculture skills pre-K through twelve all four marking periods no electoral no electives nothing less than Monday Through Friday

  • @phillipnicholas674
    @phillipnicholas6745 жыл бұрын

    Yawnnnn.

  • @williamguillen4113
    @williamguillen41134 жыл бұрын

    Too long video.

  • @thomasbulgarelli1443
    @thomasbulgarelli14434 жыл бұрын

    Why don't you buy a decent compass instead of using the piece of junk you are using!

  • @mefrym6393

    @mefrym6393

    3 жыл бұрын

    Because, he's creative

  • @abhijeetdutta6156
    @abhijeetdutta6156 Жыл бұрын

    Beautiful ❤️