Curiosity about infinity in geometry(Not homework just curious)

caters
Messages
229
Reaction score
10
Okay, let's say you have an infinitely long line segment.

Using area and volume formulas for different shapes, would you get an infinitely large shape that the formula was for in the first place?
Area:
For rectangles, would you get an infinitely large rectangle with A = l * w?
What about triangles with 1/2 * b * h?
What about squares with l^2
what about rombi with A = b * h?
what about trapezoids with A = ((b1 + b2)*h)/2?
what about pentagons with A = 5/2 * l * a(apothem)?
hexagons with A = (3√3 s2)/ 2?
what about other regular polygons with Area = (a(apothem) x p(perimeter))/2?
what about ellipses with π * vertical radius * horizontal radius?
What about circles with π * r^2
Volume:
What about spheres with V = ⁴⁄₃πr³?
What about triangular prisms with 1/2 x b x h x l?
what about other prisms with V = area of base * l (yes that includes the cylinder at the infinite end)?
what about dodecahedrons with (15+7×√5)/4 × (Edge Length)^3
what about octahedrons with (√2)/3 × (Edge Length)^3
what about Icosahedrons with 5×(3+√5)/12 × (Edge Length)^3
What about toruses that have holes with 2 × π^2 × R(radius of hole) × r^2(radius of circular cross section)?
What about cones with π × r^2 × (h/3)?
 
Mathematics news on Phys.org
What do you think?
 
I think that you would get an infinitely large shape from an infinitely long line segment but I honestly don't know.
 
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.

Similar threads

Back
Top