1. A

    imaginary golden ratio

    The post on the imaginary golden ration looks interesting, but the formulas do not display on my Chrome browser. Is there anything I should do to display the formulas?
  2. Xxmarijnw

    Why does this approach the golden ratio?

    Hi. If you pick any two number, say for instance 5 and 7 and you keep adding them together (much like the Fibonacci Sequence) you get this: 5, 7, 12, 19, 31, 50, 81, 131, ... and so on. The ratio between the last two numbers always approaches the golden ratio, no matter which set of...
  3. L

    Radius circumscribing Golden Rectangle

    Is there any significance to the radius of the circle which circumscribes the Golden Rectangle?
  4. B

    Golden ratio must be exact?

    Golden Ratio Gist and Brent method both uses golden ratio factor. This factor must be exact? I changed from 0.618 to 0.5 and next to 0.6 and I thought that will be only slower converge but new factor give me not exact results. This is important, because I am planning use multiprecision library...
  5. R

    intersection point between Golden spiral and line segment

    Greetings how can i calculate the intersection point between golden spiral and a line segment ? what i came to so far is: parametric line equation P1 + t*(P2 - P1) golden spiral equation Euler^(0.30634892761115*t) Euler^(0.30634892761115*t) = P1 + t*(P2 - P1) from here can...
  6. A

    The Golden Ratio in a Circle, Triangle, and Square: simple geometry/trigonometry cons

    I believe that I have found the golden ratio in the below figure. Geogebra is saying it is very close. Might anyone have a geometric/trigonometric proof? An equilateral triangle ABC is inscribed in a square so that segment AD is equal to segment DB. A circle is then inscribed so that it...
  7. H

    The golden rectangle

    Hi everyone, I have a math problem to solve for. It says an area rug is shaped like a golden rectangle. It's length is 8 ft. What's the rug's width? Write your answer in simplified radical form and rounded to the nearest tenth of a foot. I made a diagram but I don't know where to go from there...
  8. D

    constants like golden ratio that are used in area?

    Hi. I've heard many uses of golden ratio for artistic purposes such as in paintings, architectures and etc. It seems like the golden ratio is only used in one dimensions; usually it's used on proportions of rectangles. Are there common constants like golden ratio that are used in two...
  9. N

    Why is the golden ratio in w shaped quartics?

    Does anyone know why the golden ratio (phi and varphi) lurk in W-shaped quartics? is there some kind of mathematical calculation to see how the golden ratio is within the quartic?
  10. W

    The Golden Ratio

    Question is attached. I dont know how to find the golden ratio:eek: I really did try to solve this one, but i couldnt please please help me out
  11. S

    Unique Integer Mapping with Phi and the Golden Angle

    One of the most interesting properties of the golden ratio is it's supreme irrationality above all others. Of course, the golden angle is essentially nothing more than a restatement of phi so the same holds true for it as well. Now it may not seem from the outset that this property could...
  12. P

    Parallels of the golden section and the Eulerian number

    Helo, i don´t know what is the meaning of this, maybe someone have some ideas?!? Best regards from Germany! Rene
  13. B

    Golden Gate Bridge

    The golden gate bridge in San Francisco is 2,7 km long. The length between the towers are 1280 meters and the towers are 152 meters high (from the road to the top) The lowest point of the cables lies in the middle of the towers and on the road. It can be shown that the cables between the towers...
  14. G

    golden ratio

    Ok I am really confused about one aspect of looking at polygons. Why is it that only odd polygons show properties relating with the golden ratio? For example, the diagonals of odd polygons satisfy the relation; x-y=1/x where x=longest diagonal and y=second longest diagonal. Why can't it be with...
  15. Y

    Trying to graph Phi (the golden ratio)

    I'm doing a project in a math fair, called PJAS where you present a project to judges. I chose this project I'm confused on something though and I don't know where to start, my algebra teacher couldn't help me on it. The project says to...
  16. H

    Does the Golden Spiral pass through the 4th vertex???

    Hey Everyone:) I wasnt exactly sure which catergory this fitted by it involves complex analysis so i choose this one :) Okay my problem is in bold, the other questions i have solved but i just put them up there for background information just incase it was needed: Using a golden triangle of...
  17. V

    Golden number ratio Is there something special about the number 1.618? I'm scared, I think I'll let you mathematicians decide. :shock: Could Islam be the real deal?
  18. A

    Imaginary Golden Ratio

    We all know the Golden Ratio. \Phi=\frac{a}{b}=\frac{a+b}{a} \Phi^2-\Phi-1=0 \Leftrightarrow \Phi = \frac{1 \pm \sqrt{5}}{2} The Golden Ratio has all sorts of interesting properties like: * subsequent powers of the Golden Ratios are summable (so-called "recurrence relation"); * there exists a...
  19. D

    Golden Ratio

    I guess all, most, or many, will be familiar with the *golden ratio*, fibonacci series, etc. From the ratio we can establish that A/B = B/A+B. This is a simple algebraic formula, and we know for a fact that for this equation to be true, A / B = 0 or 1.61803399 . My question is this - using no...
  20. X

    Discovered interesting property of phi? (golden ratio)

    I was playing around with the golden section on my TI-83 in math today when I noticed something peculiar. I'm not sure if this has already been stumbled on or not but I find it interesting. Phi is the only solution to the following polynomial equations: X^2-X-1=0...