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July 16

Sum of all integers from 1-100

I remember hearing about how one famous mathematician, from the 1800s, I believe, was asked in class when he was about 13 to sum all the integers from 1-100, and within a few seconds gave the answer as 5050. Rather than try to manually sum 1+2+3+4…, he figured out that you can add up the numbers in pairs like 100+1, 99+2, 98+3, et cetera, all of which add up to 101, and of which there are 50, so the answer is 50 x 101. I don’t remember which mathematician it was, though I feel like it was Cantor or Gödel or someone from that general time period. Does anyone know who this was? Cheers, 𝔰𝔥𝔞𝔡𝔢𝔰𝔱𝔞𝔯 ^{(𝔱𝔞𝔩𝔨)} (any/all) In solidarity. 22:38, 16 July 2026 (UTC)+1

Carl Friedrich Gauss, allegedly, though it seems to be anecdotal. [1] AndyTheGrump (talk) 22:43, 16 July 2026 (UTC)

Thanks! (It was bugging me beyond belief not being able to remember.) Cheers, 𝔰𝔥𝔞𝔡𝔢𝔰𝔱𝔞𝔯 ^{(𝔱𝔞𝔩𝔨)} (any/all) In solidarity. 22:47, 16 July 2026 (UTC)

July 24

Geodesic n-dimension distance calculation

I was looking at distance calculations like all the p-value Minkowski distances, and I looked at geodesic distance. If radius is the same for every dimension (a circle in 2D, a sphere in 3D, a hypersphere in nD), the formula to calculate the shortest distance between two points (defined as vectors from origin) is easy. What if every dimension had it's own radius? I'm thinking about Earth. The first two dimensions have the same radius (creating the equator), but the third is shorter (the polar radius). If I wanted 4D, 5D, 6D? Is there a single formula where I can use the angle definitions of two vectors and a list of the radii and calculate the shortest distance along the surface of the curved shape? ~2026-35239-54 (talk) 17:36, 24 July 2026 (UTC)

Take the case p = 2 (Euclidean distance) in two-dimensional Cartesian space. What does it mean if the two dimensions "have" their own radii – say one "has" radius a and the other radius b? Do you mean they are rolled up, topologically forming a torus? But then, why mention a circle for the case that a = b?  ​‑‑Lambiam 21:33, 24 July 2026 (UTC)

Our article on ellipse describes a shape with a larger and smaller diameter. One is in one dimension (height) and the other is in another dimension (width). It mentions no confusion with a torus. ~2026-39968-68 (talk) 21:56, 24 July 2026 (UTC)

I do not think that there is any simple formula for the distance along a geodesic on an ellipsoid or spheroid. You will just have to integrate the metric numerically. JRSpriggs (talk) 22:48, 24 July 2026 (UTC)

There is not even a simple formula for the 2D case of the arc length along a segment of an ellipse.  ​‑‑Lambiam 10:08, 25 July 2026 (UTC)

I know you're referring to ellipsoids beyond just three dimensions, but geodesics on an ellipsoid might help for the 3D case. GalacticShoe (talk) 00:45, 25 July 2026 (UTC)

You could try using the calculus of variations and apply the constraint of staying on the ellipsoid with a Lagrange multiplier. This would give you a difficult set of differential equations to solve. JRSpriggs (talk) 11:42, 25 July 2026 (UTC)

The method from Geodesics on an ellipsoid § Geodesics on a triaxial ellipsoid should be generalizable but I'd expect it to get unpleasantly complicated. –jacobolus (t) 18:48, 25 July 2026 (UTC)

Just thinking: If the complication is recursive, it is a time/calculation complexity, not a method complexity. So, a relatively simple recursive computer function could do the estimation. ~2026-41824-87 (talk) 14:56, 27 July 2026 (UTC)

In computer science, "recursive function" has several unrelated meanings.

The calculation comes down to computing a definite integral of a function that is not only complicated in terms of how many symbols are needed to write down its definition, but more so (and I think this is what was meant) in how much work it will be to determine the correct form of this function. This is not a job for the faint of heart – but perhaps someone has already done the work.  ​‑‑Lambiam 17:51, 27 July 2026 (UTC)

I assumed it was obvious by context I was referring to self-referential, repeating logic where computational complexity scales with depth. ~2026-41824-87 (talk) 17:59, 27 July 2026 (UTC)