https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Mathematics sorted by active. https://community.wolfram.com/groups/-/m/t/3756713 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/e3736d85-b2dd-44c5-b768-4d05ec81c9bc Alejandro Latorre Chirot 2026-07-12T15:27:21Z https://community.wolfram.com/groups/-/m/t/3756704 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/bbde10ea-edca-4edc-bf6e-87d897509094 Alejandro Latorre Chirot 2026-07-12T15:22:15Z https://community.wolfram.com/groups/-/m/t/3756631 Limit[(t^2 (-1 + t^k))/(-1 + t), k -> +Infinity] // FullSimplify[#, 0 < t < 1] & The code is not correctly calculating the right limit value, where the parameter t ranges from 0 < t < 1. The correct result should be t²/(1 - t). How can this be obtained? Wen Dao 2026-07-12T02:50:44Z https://community.wolfram.com/groups/-/m/t/3756371 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/b865cc51-dfe0-4120-b064-954f66c0f01c Alejandro Latorre Chirot 2026-07-11T22:34:37Z https://community.wolfram.com/groups/-/m/t/3756327 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/adf6c134-2522-4e40-9530-169a4f560c81 Ed Pegg 2026-07-11T14:29:15Z https://community.wolfram.com/groups/-/m/t/3752149 ![Spectral universality of deficit-angle curvature in Regge Laplace-Beltrami geometry][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WSRPThumbnailProject.png&userId=3749899 [2]: https://www.wolframcloud.com/obj/8ff2c8d8-86c9-425c-89a2-3a8149cd0881 Arnav Mittal 2026-07-09T20:38:24Z https://community.wolfram.com/groups/-/m/t/3755693 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ec23aaee-5ccf-4a58-80f4-89308128cec2 Alejandro Latorre Chirot 2026-07-10T21:43:08Z https://community.wolfram.com/groups/-/m/t/3755908 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/dd61d583-aa72-4df5-b6a1-878009859a83 Alejandro Latorre Chirot 2026-07-10T21:28:09Z https://community.wolfram.com/groups/-/m/t/3755592 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/e827c398-ac5b-4aa9-b68a-54d70a432fd4 Alejandro Latorre Chirot 2026-07-10T16:13:24Z https://community.wolfram.com/groups/-/m/t/3754408 ![Partial Cayley graph for SL_2(Z/(7^3)) consisting of words of length up to 12 in two generators.][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=herophoto.png&userId=3753998 [2]: https://www.wolframcloud.com/obj/0eae72ba-0222-4050-a378-822688cfd80d Henry Lewis 2026-07-10T01:40:09Z https://community.wolfram.com/groups/-/m/t/3754125 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-09at7.30.59%E2%80%AFPM.png&userId=3753710 [2]: https://www.wolframcloud.com/obj/5286a4e2-cc4f-4e10-a63c-53f17625aec7 Warren Chen 2026-07-10T00:58:00Z https://community.wolfram.com/groups/-/m/t/3752960 ![enter image description here][1]&[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-09at4.43.00%E2%80%AFPM.png&userId=3751786 [2]: https://www.wolframcloud.com/obj/732dc46b-df9c-4831-a7e2-796b38b0d018 Gracelyn Chen 2026-07-09T22:40:07Z https://community.wolfram.com/groups/-/m/t/3753019 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=newPunch.png&userId=3751686 [2]: https://www.wolframcloud.com/obj/68ce705c-3c97-4c66-ae86-d52da6b6dcf5 Nicholas Zhan 2026-07-09T21:41:31Z https://community.wolfram.com/groups/-/m/t/3752071 ![image][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-09at4.33.15%E2%80%AFPM.png&userId=3740316 [2]: https://www.wolframcloud.com/obj/bbf6661d-dc8c-4d9d-b452-28004d2dd42c Saanvi Raghavendran 2026-07-09T21:05:57Z https://community.wolfram.com/groups/-/m/t/1141202 The Demonstration [Ponting Square Packing](http://demonstrations.wolfram.com/PontingSquarePacking/) can arrange sequentially sized squares into an asymmetric shape. I've often wondered if the method could be used to obtain symmetry. Turns out that subtracting half gives half a lune. For the below I started with an arrangement of 19^2 = 361 squares, then subtracted 181. That gives a half lune where all squares of size 1 to 180 are represented twice. Make another copy and the 720 squares (four copies of squares 1 to 180) will make a lune. ![sequential square lune][1] I suppose it's actually a lens. ![1984][2] I figured out that curve, mostly. It's a hyperbola. I still haven't figured out the optimal way to fit the two pieces together with a unifying curve. But here's a stab at it. squarepoly[{corner_, size_}] := Table[corner, {4}] + {{0, 0}, {0, size}, {size, size}, {size, 0}}; pontingMatrix[order_Integer] := Reverse[Reverse /@ (Partition[Reverse[If[IntegerQ[#], #, 0] & /@ (#/2 + 1/2 & /@ Range[(2 order + 1)^2])], (2 order + 1)] +Reverse /@ Transpose[Partition[ If[IntegerQ[#], # + ((2 order + 1)^2 + 1)/2, 0] & /@ (#/2 & /@Range[(2 order + 1)^2]), (2 order + 1)]])]; Module[{pm, xx, yy, alt, r1n, rn1, rad, numbers, squares1, squares2, offset1, offset2, siz, order, count}, siz = 31; order = (2 siz + 1); count = (order^2 - 1)/2; pm = pontingMatrix[siz] - (count + 1); numbers = False; xx = 2 siz + 1; yy = 2 siz + 1; alt = Flatten[Append[Table[{1, -1}, {siz}], 1]]; r1n = Transpose[{FoldList[Plus, 0, Drop[ pm[[1]], -1]],Drop[Flatten[{#, #} & /@ (First /@ Partition[Append[FoldList[Plus, 0, Drop[alt pm[[1]], -1]], 0], 2])], 1]}]; rn1 = Transpose[{Drop[Flatten[{#, #} & /@ (First /@ Partition[ Append[FoldList[Plus, 0, Drop[alt, -1] Drop[ Transpose[pm][[1]], 1]], 0], 2])], -1], FoldList[Plus, 0, Drop[ Transpose[pm][[1]], -1]]}]; rad = Table[If[Min[{a, b}] == 1, {0, 0}, If[OddQ[a + b], {0, pm[[a - 1, b]]}, {pm[[a, b - 1]], 0}]], {a, 1,xx}, {b, 1, yy}]; rad[[1, 1]] = {0, 0}; Do[rad[[1, nn]] = r1n[[nn]]; rad[[nn, 1]] = rn1[[nn]], {nn, 2, xx}]; Do[If[OddQ[a + b], rad[[a, b]] = rad[[a - 1, b]] + rad[[a, b]], rad[[a, b]] = rad[[a, b - 1]] + rad[[a, b]]], {a, 2, xx}, {b, 2, yy}]; offset1 = {88650, 0} - (squarepoly[{rad[[1, 63]], pm[[1, 63]]}].N[RotationMatrix[-78/100 - Pi/2]])[[3]]; offset2 = {-88650, 0} - (squarepoly[{rad[[1, 63]], pm[[1, 63]]}].N[RotationMatrix[-78/100 + Pi/2]])[[3]]; squares1 = Table[{Hue[.3 + Abs[pm[[a, b]]]/count], Polygon[(# + offset1 & /@ (squarepoly[{rad[[a, b]], pm[[a, b]]}].N[ RotationMatrix[-78/100 - Pi/2]]))]}, {a, 1, xx}, {b, 1, yy}]; squares2 = Table[{Hue[.3 + Abs[pm[[a, b]]]/count], Polygon[# + offset2 & /@ (squarepoly[{rad[[a, b]], pm[[a, b]]}].N[ RotationMatrix[-78/100 + Pi/2]])]}, {a, 1, xx}, {b, 1, yy}]; Graphics[{EdgeForm[{Black, Thin}], squares1, squares2, Plot[45200 - 5.04953`*^-17 x - 5.64864`*^-6 x^2, {x, -89316.1`, 89316.1}, PlotStyle -> {Thickness[0.003], Darker[Gray]}][[1]], Plot[-45200 + 5.04953`*^-17 x + 5.64864`*^-6 x^2, {x, -89316.1, 89316.1}, PlotStyle -> {Thickness[0.003], Darker[Gray]}[[1]]}, ImageSize -> {1200, 600}]] ![Squares 1 to 1984, each 4 times, bounded by hyperbola][3] There should be a way to recursively optimize the (rotation, fit, offsets) for the hyperbolas. After that, clashing squares in the middle could be moved to voids near the hyperbolas, then more recursion. [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=squarelune.jpg&userId=21530 [2]: http://community.wolfram.com//c/portal/getImageAttachment?filename=1984.jpg&userId=21530 [3]: http://community.wolfram.com//c/portal/getImageAttachment?filename=1035EyeofPonting.jpg&userId=21530 Ed Pegg 2017-07-07T21:34:11Z https://community.wolfram.com/groups/-/m/t/2952778 I would like to be able to explore if certain variable coefficient differential operator commute with integral operators. As a toy example Grünbaum (Grünbaum, F. Alberto. "A remark on Hilbert's matrix." Linear Algebra and its Applications 43 (1982): 119-124.) mentions that on L^2[0.1] the integral operator K with kernel 1/(x+y) commutes with the differential operator P where Pu (t) = ((1-t^2)t^2 u')' -2 t^2 u I wanted to make a pure function for the operators for example K = Function[f, Function[t, Integrate[f[s]/(t + s), {s, 0, 1}]]] and similarly P and then to be able to evaluate the commutator with something like K@*P - P@*K By hand it is fairly easy and uses integration by parts, but obviously I want to do much more complicated cases! The difficulties I have are that Mathematica will not simplify the composition of operators, unless applied to a function, and then only a specific function. And it does not understand subtraction of operators. Am I going about this the wrong way? Is it something Mathematica can do. So far I verified in on a Fourier basis in L^2 with Mathematica, it generates two pages of output but FullSimplify gets it to zero. William Lionheart 2023-07-06T11:48:29Z https://community.wolfram.com/groups/-/m/t/3021398 In Python or Matlab, the eigensolver can solve the system by giving the linear function (for example, in Matlab we can use eigs(Afun,...)), this speeds up the calculation largely as we do not need to construct the whole matrix. I can not find a similar solver in Mathematica. I wonder if there is a way to achieve this within Mathematica. Any ideas would be appreciated. Frank Xu 2023-09-26T06:00:42Z https://community.wolfram.com/groups/-/m/t/3739392 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/c3fad79c-0458-4901-8177-944b192d22da Robert Rimmer 2026-06-27T01:40:35Z https://community.wolfram.com/groups/-/m/t/366628 POSTED BY: ======== **Marvin Ray Burns, and distinguished colleagues** ---------- My exciting experiences using Wolfram technologies! --------------------------------------------------- ---------- The MRB constant, a fascinating mathematical anomaly, has intrigued researchers and enthusiasts alike for decades. Defined as the limiting value of a unique alternating series, this enigmatic constant showcases the beauty of numerical exploration and convergence. Despite its relatively recent emergence, the MRB constant reveals unexpected connections to various fields within mathematics and computational analysis. In this post, we dive into its origins, properties, and the ongoing quest to uncover its more profound significance. The MRB constant is an anomaly because it emerges from an alternating series with unusual convergence behavior. Unlike many well-known mathematical constants, the MRB constant has no closed-form expression nor a known exact nature—whether it is algebraic, transcendental, or even irrational. Additionally, the sequence of partial sums that define the MRB constant oscillates between two limit points, creating a bounded yet divergent behavior. This oscillatory nature distinguishes it from more conventional mathematical constants, which typically exhibit straightforward convergence. Its mysterious properties continue to intrigue mathematicians as they explore its deeper connections to number theory and computational analysis. ---------- ---------- CMRB ![If you see this instead of an image, reload the page][1] **is the MRB constant.** Without solicitation, GPT echoed one of this discussion's contributors and gave a shoutout to Mathematica's accomplishments by saying: ------------------- > > **Why Computing Digits of the MRB Constant Is Interesting** > > At first glance, the computation of ever more digits of a numerical > constant may appear to be a sterile exercise, offering little insight > beyond the digits themselves. For the MRB constant, this > interpretation is profoundly misleading. The interest lies not in the > digits, but in the act of computing them. > > The MRB series occupies a delicate numerical regime: it is convergent, > yet only marginally so; its terms are elementary in form, yet hostile > to naive numerical evaluation; and its alternating structure conceals > severe cancellation effects. As a result, each additional digit of > accuracy is not merely an extension of a decimal expansion, but a > validation of the mathematical and algorithmic framework used to > obtain it. > > In this sense, the digits serve as a stress test for mathematics > itself. They expose the difference between formal convergence and > effective convergence, between theoretical existence and computational > feasibility. Techniques that are elegant on paper often fail > catastrophically in practice, while successful methods must balance > asymptotics, numerical stability, precision control, and computational > cost. > > Moreover, the computation of the MRB constant forces the > reconciliation of disparate mathematical ideas. Alternating series, > logarithmic asymptotics, convergence acceleration, special functions, > and analytic continuation must all agree numerically. Any hidden > inconsistency—whether conceptual or computational—reveals itself > immediately in the failure of the digits to stabilize. > > Thus, computing digits of the MRB constant transforms mathematics from > a static collection of statements into a living experiment. The > resulting digits are not trophies; they are evidence. They measure the > effectiveness of our methods, the soundness of our assumptions, and > the practical reach of our theory. > > In short, the digits themselves do not matter. What matters is that > they *can* be computed at all—and how difficult it is to do so. > That difficulty is precisely what makes the MRB constant > mathematically interesting. **In general, we will see:** ![enter image description here][7] ---------- ---------- ---------- [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-25023042.png&userId=366611 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-01-01235656.png&userId=366611 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-01-01235710.png&userId=366611 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-02-18190718.png&userId=366611 Marvin Ray Burns A.G.S. (cum laude) 2014-10-09T18:08:49Z https://community.wolfram.com/groups/-/m/t/3719376 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=_erdos_AI_ChatGPT.gif&userId=11733 [2]: https://www.wolframcloud.com/obj/dab42afe-f890-46cd-b849-40c304ebf581 Ed Pegg 2026-05-21T03:41:56Z