MHB Help Me Solve the Golden Ratio Question

  • Thread starter Thread starter wrightarya
  • Start date Start date
  • Tags Tags
    Golden ratio Ratio
wrightarya
Messages
4
Reaction score
0
Question is attached.
I don't know how to find the golden ratio

I really did try to solve this one, but i couldnt
please please help me out
 

Attachments

  • Untitled picture 2.png
    Untitled picture 2.png
    19.4 KB · Views: 111
Mathematics news on Phys.org
wrightarya said:
Question is attached.
I don't know how to find the golden ratio

I really did try to solve this one, but i couldnt
please please help me out

Call length AB = x and BC = y. Since AYXD is a square, that means length YB = x - y. Because the two rectangles are similar, their sides are in proportion, so

$\displaystyle \begin{align*} \frac{x}{y} &= \frac{y}{x - y} \\ x \left( x - y \right) &= y^2 \\ x^2 - x\,y &= y^2 \\ x^2 - x\,y + \left( -\frac{y}{2} \right) ^2 &= y^2 + \left( -\frac{y}{2} \right) ^2 \\ \left( x - \frac{y}{2} \right) ^2 &= \frac{4y^2}{4} + \frac{y^2}{4} \\ \left( x - \frac{y}{2} \right) ^2 &= \frac{ 5y^2}{4} \\ x - \frac{y}{2} &= \frac{\sqrt{5}\,y}{2} \\ x &= \frac{y + \sqrt{5}\,y}{2} \\ x &= \left( \frac{1 + \sqrt{5}}{2} \right) \, y \end{align*}$
 
Last edited:

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

B Golden Ratio in Collatz-like sequences
Replies
1
Views
2K
I Is e^pi a unique transcendental, or perhaps not transcendental?
Replies
1
Views
2K
I Fibonacci Series and Golden Ratio Explained
Replies
3
Views
2K
B Understanding the relationship between ratios and fractions
Replies
8
Views
2K
InWhat Situations Do We Enounter the Golden Ratio?
Replies
10
Views
2K
B Sequence formula needed - Keyword --> annuity
Replies
10
Views
2K
B Cross section (?) of Great Pyramid from drone footage
Replies
47
Views
5K
MHB Ratio of areas of squares - Challenging problem
Replies
1
Views
2K
MHB Is the Golden Ratio Integral to Solving Trigonometric Integrals?
Replies
5
Views
2K
I How Can You Calculate the First 50 Digits of the Golden Ratio in Hexadecimal?
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top