MHB Radius Small Circle: Measurement & More

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Circle Radius
Albert1
Messages
1,221
Reaction score
0

Attachments

  • radius of small circle.jpg
    radius of small circle.jpg
    25.8 KB · Views: 97
Mathematics news on Phys.org
[sp]Let suppose that the side of the square is 2. In this case, if x is the radius of the 'small circle', for the theorem of Pythagoras it must be...

$\displaystyle (1-x)^{2} + 1 = (1+x)^{2}$

... so that is $\displaystyle x = \frac{1}{4}$...[/sp]

Kind regards

$\chi$ $\sigma$
 
hint:
see Ford Circles
 
chisigma said:
[sp]Let suppose that the side of the square is 2. In this case, if x is the radius of the 'small circle', for the theorem of Pythagoras it must be...

$\displaystyle (1-x)^{2} + 1 = (1+x)^{2}$

... so that is $\displaystyle x = \frac{1}{4}$...[/sp]

Kind regards

$\chi$ $\sigma$
very good solution !
 

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 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB Calculate the radius of the circle
Replies
5
Views
2K
I Is the Ratio of Circumference to Radius of a Circle Always Irrational?
Replies
19
Views
2K
B Why does the radius of a unit circle need to be 1?
Replies
36
Views
5K
MHB Relationship between inner and outer radius of a two concentric circles
Replies
2
Views
2K
MHB Area of multiple circles inside a rectangle
Replies
3
Views
2K
B Circle tangent to two lines and another circle
Replies
2
Views
2K
B Understanding why πr^2 works for different area calculations
Replies
7
Views
2K
B Strange Relationships of the Circle
Replies
10
Views
1K
B Do I have enough information to find the radius?
Replies
16
Views
2K
B How to find a length of a "radius" not centered in a circle?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top