How to find the area enclosed by four circular pieces touching each other?

  • Thread starter Thread starter suhaskowshik_92
  • Start date Start date
  • Tags Tags
    Areas
suhaskowshik_92
Messages
4
Reaction score
0
Four circular cardboard pieces each of radius 7cm are placed in such a way that each piece touches two other pieces.Find the area of the encosed by the four pieces.Can anyone help me to solve this problem?
 
Mathematics news on Phys.org
1. Draw a diagram

2. Join the centers of the 4 circles to form a square.

3. Look at it and work out what area you need to subtract from the sqaure in order to leave the desired "enclosed area" remaining.
 
Alternatively, it should be pretty obvious that the enclosed area is four times a sector given by a circle circumscribed inside a square.
 
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...
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...
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.
Back
Top