Talk:Surface area

Two dimensions

Is it really correct that two dimensional structures such as triangles have "surface area" ? I do not think so, "surface area" is a three dimensional concept. Ar

I've moved the table of areas of plane figures to the talk page of "Area". Arcfrk (talk) 08:48, 11 March 2008 (UTC)

Surface Area To Volume Ratios

There is a problem with the last section. It states that if you increase the radius the ratio decreases. However, if you change the units of measure, the ratio can increase with a larger radius. A radius of 100 meters has a SA:V ratio of .03, but a radius of 1 kilometer has a ratio of 3. Also, it should be clear that this is assuming cells have a spherical shape. —Preceding unsigned comment added by 70.188.231.137 (talk) 04:05, 30 March 2008 (UTC)

SA:V is measured in inverse distance units. It is not dimensionless. A sphere with a radius of 100 meters has a ratio of 0.03/meter while the sphere with a radius of 1 kilometer has a ratio of 3/kilometer = 3/(1000 meters) = 0.003/meter. Measuring in the same units, the sphere ten times larger has a ten times smaller ratio, as it should. This similarity law holds for any shape, not just spheres. In the case of cells the only assumption is that a big cell is the same shape as a little one. This is more or less true of cells. It is definitely not true of multicellular structures, which is why one can easily distinguish a mouse bone from an elephant bone even when the mouse bone is magnified to elephantine size. -Dmh (talk) 05:32, 23

And I am SMART —Preceding unsigned comment added by 66.112.37.98 (talk) 22:33, 2 March 2011 (UTC)

What. The. Hell.

I came here to verify a formula, but I ended up stumbling upon a page a 4th grader could have written. What in the world happened to this article?

S lijin (talk) 01:54, 19 May 2009 (UTC)

I came here to verify a formula, but I ended up stumbling upon a page a professor could have written. What in the world happened to this article? i can not understand any of this, perhaps someone could submit something eaiser to understand Summer911 (talk) 05:32, 10 March 2010 (UTC)

Moved from the article

Shape

Area formula derivation

Sphere

The surface area of a sphere is the integral of infinitesimal circular rings of width $dx$ The radius of the circular ring is $f(x)={\sqrt {r^{2}-x^{2}}}$. The length of the circular ring is equal to $2\pi \cdot f(x)$ The width of the ring can be determined by using Pythagoras' formula for a rectangular triangle with side lengths $dx$ and $f'(x)\cdot dx$, which leads to ${\sqrt {1+f'(x)^{2}}}\,dx$ The infinitesimal surface area of the circular ring thus is equal to $2\pi f(x)\cdot {\sqrt {1+f'(x)^{2}}}\,dx$ The derivative of $f(x)$ is equal to $f'(x)={\frac {-x}{\sqrt {r^{2}-x^{2}}}}$ The surface area of the sphere can be calculated as $\int _{-r}^{r}2\pi f(x)\cdot {\sqrt {1+f'(x)^{2}}}\,dx$ = $\int _{-r}^{r}2\pi {\sqrt {r^{2}-x^{2}}}\cdot {\sqrt {(}}1+{\frac {x^{2}}{r^{2}-x^{2}}})\,dx=\int _{-r}^{r}2\pi {\sqrt {r^{2}}}\,dx=2\pi r\int _{-r}^{r}1\,dx$ The antiderivative needed is the simple linear function $x$ Thus, the sphere surface area amounts to Asphere = $2\pi r[r-(-r)]=4\pi r^{2}$ References recovered partially http://web.archive.org/web/20120427201949/http://www.math.usma.edu/people/rickey/hm/CalcNotes/schwarz-paradox.pdf — Preceding unsigned comment added by 94.197.120.122 (talk) 22:10, 9 October 2013 (UTC) http://web.archive.org/web/20111215152255/http://mathdl.maa.org/images/upload_library/22/Polya/00494925.di020678.02p0385w.pdf — Preceding unsigned comment added by 94.197.120.122 (talk) 22:19, 9 October 2013 (UTC) External links modified Hello fellow Wikipedians, I have just modified one external link on Surface area. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes: Added archive https://web.archive.org/web/20111215152255/http://mathdl.maa.org/images/upload_library/22/Polya/00494925.di020678.02p0385w.pdf to http://mathdl.maa.org/images/upload_library/22/Polya/00494925.di020678.02p0385w.pdf When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs. This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 18 January 2022). If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool. If you found an error with any archives or the URLs themselves, you can fix them with this tool. Cheers.—InternetArchiveBot (Report bug) 18:22, 26 July 2017 (UTC) Should "Surface Measure" redirect here? The technical term "surface measure" doesn't have a wikipedia page. Is this the page? Should a redirect come here? Characterization The article mentions a characterization of surface area using a few properties such as additivity and invariance under Euclidean motions. There should be given a source for this, and preferably it should also be explained more clearly. MathHisSci (talk) 21:52, 14 April 2023 (UTC)