https://community.wolfram.com RSS Feed for Wolfram Community showing ideas tagged with Wolfram|Alpha with no replies sorted by active. https://community.wolfram.com/groups/-/m/t/3758832 Introduction In this post I use Wolfram technologies and Wolfram Language syntax to investigate an exact algebraic chain connecting the constants 4096, 1729, and an eighteenth-root operator arising in my mathematical investigations. The purpose of this post is to illustrate symbolic computation and high-precision numerical verification using Wolfram technologies. All symbolic computations presented below are expressed in Wolfram Language syntax and verified using Wolfram computational technologies. Step 1. Exact symbolic identity expr = (Sqrt[2 - Sqrt[3]] - Sqrt[2 + Sqrt[3]])^24; FullSimplify[expr] Output: 4096 Step 2. Hardy–Ramanujan number ramanujan = 27*Sqrt[expr] + 1; FullSimplify[ramanujan] Output: 1729 Step 3. Eighteenth-root operator operator = (expr + ramanujan)^(1/18); N[operator,50] Output: 1.618762396... Step 4. Comparison with the Golden Ratio N[GoldenRatio,50] N[operator - GoldenRatio,50] The second command computes the numerical difference between the algebraic operator and the Golden Ratio. Step 5. High-precision computation N[operator,100] This confirms the stability of the numerical value at arbitrary precision. Visualization Plot[ (4096 + 1729)^(1/x), {x,10,25}, PlotRange->All, AxesLabel->{"Exponent","Value"} ] The graph illustrates how the algebraic operator evolves as the exponent varies. Conclusion This post illustrates how Wolfram Language can be used for exact symbolic computation, arbitrary precision arithmetic, numerical verification, visualization of algebraic operators. The complete symbolic chain 4096 ↓ 1729 ↓ (4096 + 1729)^(1/18) ↓ 1.618762396... is obtained through Wolfram technologies using Wolfram Language syntax. ![enter image description here][1] ![enter image description here][2] The accompanying Wolfram|Alpha evaluations confirm the exact symbolic identities and the corresponding high-precision numerical values, illustrating the effectiveness of Wolfram technologies for symbolic mathematical exploration. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-14154755.png&userId=2483773 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-07-14155008.png&userId=2483773 Michele Nardelli 2026-07-14T14:08:26Z https://community.wolfram.com/groups/-/m/t/3659892 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/fab0aaa2-5d63-4566-8eca-4240f66f7920 Daniel Carvalho 2026-03-14T01:14:56Z https://community.wolfram.com/groups/-/m/t/3599693 The current Wolfram Alpha Pro MathML File Upload example is OK, but ... https://www.wolframalpha.com/input?i=display+form&fileId=c3f74f5f-fa51-492e-85a8-799a434ab84f I found a better one! Stewart Dickson 2026-01-01T22:35:54Z https://community.wolfram.com/groups/-/m/t/3471630 &[Wolfram Notebook][1] Interestingly, - The sequence (-1)^n(n^(1/n)-1) is not "open" in the sense that it doesn't diverge or expand indefinitely. Instead, it oscillates . - It is not "closed" either for individual terms, because they do not settle into a single value or a finite set of values. Instead, we focus on the convergence of the series formed by these terms, which leads to the MRB constant. [1]: https://www.wolframcloud.com/obj/37cc3458-d4ab-4185-beaa-9fff64fa3417 Marvin Ray Burns A.G.S. (cum laude) 2025-05-30T23:02:03Z https://community.wolfram.com/groups/-/m/t/3465731 ![enter image description here][1] ![enter image description here][2] ![enter image description here][3] ![enter image description here][4] ![enter image description here][5] ![enter image description here][6] ![enter image description here][7] ![enter image description here][8] ![enter image description here][9] ![enter image description here][10] ![enter image description here][11] ![enter image description here][12] ![enter image description here][13] ![enter image description here][14] ![enter image description here][15] ![enter image description here][16] ![enter image description here][17] ![enter image description here][18] ![enter image description here][19] ![enter image description here][20] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22120454.png&userId=2483773 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22120803.png&userId=2483773 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22121041.png&userId=2483773 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22121406.png&userId=2483773 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22121740.png&userId=2483773 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22121852.png&userId=2483773 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22122121.png&userId=2483773 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22125335.png&userId=2483773 [9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22125506.png&userId=2483773 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22125559.png&userId=2483773 [11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22125723.png&userId=2483773 [12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22125909.png&userId=2483773 [13]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22130151.png&userId=2483773 [14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22130507.png&userId=2483773 [15]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22130638.png&userId=2483773 [16]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22132312.png&userId=2483773 [17]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22132422.png&userId=2483773 [18]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22132540.png&userId=2483773 [19]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22133237.png&userId=2483773 [20]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-05-22133411.png&userId=2483773 Michele Nardelli 2025-05-22T11:35:20Z https://community.wolfram.com/groups/-/m/t/3457583 From this other version of Master equation ![enter image description here][1] We obtain, considering the integral tending to zero: ![enter image description here][2] From which, we obtain, in conclusion: ![enter image description here][3] Again a value that is very closed to the Golden Ratio! [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ImmagineMaster.png&userId=2483773 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4701Immagine2.png&userId=2483773 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8042Immagine3.png&userId=2483773 Michele Nardelli 2025-05-08T21:15:50Z https://community.wolfram.com/groups/-/m/t/3398162 Curious about NASA's Europa Clipper mission unusual route? Watch here as we take you through the spacecraft's journey to Jupiter's moon, Europa. Don't forget to like, comment and subscribe for more exciting space content! &[Wolfram Notebook][1] Congratulations to the Jet Propulsion Laboratory Europa Clipper System Engineering Team who were awarded with the Wolfram Innovator award for their use of Wolfram Language and System Modeler to validate requirements against performance of the Clipper's thermal management system before launch. [1]: https://www.wolframcloud.com/obj/8f6fae2f-a239-44db-a246-6a2670ac856c [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ARD_YT_EuropaClipper.png&userId=1660606 [3]: https://www.youtube.com/watch?v=sqmQh_WKcPc Keren Garcia 2025-02-20T23:07:38Z https://community.wolfram.com/groups/-/m/t/3258257 I hope this message finds you well. As per your instructions from the event, I am reaching out to provide the details of my project, VitalityAI, which utilizes the Wolfram API. Here are the relevant links: - GitHub Repository: https://github.com/subhro1530/VitalityAI - Project/Website Working Link: https://vitalityai.vercel.app/chatbot - Project Demo Video: https://www.youtube.com/watch?v=Xony_HNdFGM Thank you for the opportunity! Pratham Agarwal 2024-08-27T20:26:56Z https://community.wolfram.com/groups/-/m/t/3245342 I used the Wolfram Alpha LLM API in my project "FirstGenesis" and won 5th place in Empower Hacks 2.0. It sends queries and outputs the results. Here are the Links https://devpost.com/software/firstgenu https://firstgenesis.vercel.app/ https://github.com/DracoRX16/firstgenesis/tree/main Aayush Jalgaonkar 2024-08-10T06:15:53Z https://community.wolfram.com/groups/-/m/t/3236609 I'm also attaching a screenshot of the previous calculation. https://www.wolframalpha.com/input?i2d=true&i=Power%5B2%2C%5C%2840%29%5C%2840%29Divide%5BDivide%5B%5C%2840%293%5C%2840%29n%2B2%5C%2841%29%2B1%5C%2841%29%2C2%5D%2C2%5D-Divide%5BDivide%5B%5C%2840%293Divide%5B%5C%2840%29n%2B3%5C%2841%29%2C2%5D%2B1%5C%2841%29%2C2%5D%2C2%5D%5C%2841%29-%5C%2840%29n%2B1%5C%2841%29%5C%2840%29Divide%5B3%2C8%5D%5C%2841%29%5C%2841%29%2B%5C%2840%29%5C%2840%29Divide%5BDivide%5B%5C%2840%293%5C%2840%29n%2B1%5C%2841%29%2B1%5C%2841%29%2C2%5D%2C2%5D-Divide%5BDivide%5B%5C%2840%293Divide%5B%5C%2840%29n%2B2%5C%2841%29%2C2%5D%2B1%5C%2841%29%2C2%5D%2C2%5D%5C%2841%29-%5C%2840%29n%5C%2841%29%5C%2840%29Divide%5B3%2C8%5D%5C%2841%29%5C%2841%29%2B%5C%2840%29%5C%2840%29%5C%2840%29-3%5C%2840%29-n%5C%2841%29%2B1%5C%2841%29-%5C%2840%293n%2B1%5C%2841%29%5C%2841%29%5C%2841%29%2B%5C%2840%29%5C%2840%29Divide%5B%5C%2840%29Power%5B2%2Cn%5D*3%5C%2840%29Power%5B2%2C%5C%2840%29n-1%5C%2841%29%5D%5C%2841%29%2C4%5D%5C%2841%29-%5C%2840%29Power%5B2%2C%5C%2840%29n-1%5C%2841%29%5D*3%5C%2840%29Power%5B2%2C%5C%2840%29n-2%5C%2841%29%5D%5C%2841%29%5C%2841%29%5C%2841%29%5D%3D1 Paul Charlton 2 2024-07-27T18:10:55Z https://community.wolfram.com/groups/-/m/t/3166260 https://github.com/Evadshell/Aminovate2 Github link to my project --- **Project Name:** MathQuester! **Tagline:** Your Personal Math Assistant **Description:** MathQuester! is an interactive math learning platform designed to make math learning more engaging and accessible to students of all levels. With MathQuester!, users can explore mathematical concepts, solve problems, and receive step-by-step guidance through complex equations. **Features:** - **Full Results API Integration:** Utilizing Wolfram's Full Results API, MathQuester! delivers comprehensive solutions to mathematical queries, including step-by-step solutions, visual representations, and related concepts. - **Conversational AI:** MathQuester! incorporates conversational AI to provide an interactive learning experience. Users can ask questions in natural language and receive detailed explanations and solutions. - **MathBot Integration:** In addition to text-based interaction, MathQuester! features MathBot, an AI-powered assistant that enhances interactivity through voice control and audio feedback. MathBot makes learning math more intuitive and engaging. - **OAuth2 Google Login:** Users can securely log in to MathQuester! using their Google accounts, ensuring a seamless and personalized experience. - **Chakra UI:** MathQuester! boasts a user-friendly interface built with Chakra UI, offering a sleek and responsive design across all devices. - **Future Scope:** In the future, MathQuester! aims to further enhance its interactivity and accessibility. Planned features include audio-controlled interactions, real-time collaboration tools, and personalized learning paths tailored to individual users' strengths and weaknesses. **Challenges Faced:** During development, we encountered challenges in integrating various APIs seamlessly and ensuring a smooth user experience across different platforms. However, through rigorous testing and iterative improvements, we overcame these hurdles to deliver a polished product. **Future Scope:** - **Enhanced Interactivity:** Implementing audio-controlled interactions to enable hands-free operation, catering to users with diverse needs and preferences. - **Real-time Collaboration:** Introducing collaborative features that allow multiple users to work on math problems together in real-time, fostering teamwork and peer learning. - **Personalized Learning Paths:** Utilizing machine learning algorithms to analyze user performance and provide personalized recommendations for improving math skills. Tejas keshwani 2024-04-29T04:01:44Z https://community.wolfram.com/groups/-/m/t/3070538 We analyze the following equation, concerning the enthalpy of the modified white hole. All calculations were carried out using the WolframAlpha. ![formulas][1] ![formulas][2] ![formulas][3] ![formulas][4] ![formulas][5] ![formulas][6] ![formulas][7] ![formulas][8] ![formulas][9] ![formulas][10] ![formulas][11] ![formulas][12] ![formulas][13] ![formulas][14] ![formulas][15] ![formulas][16] ![formulas][17] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=.jpg&userId=2483773 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_2.jpg&userId=2483773 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_3.jpg&userId=2483773 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_4.jpg&userId=2483773 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_5.jpg&userId=2483773 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_6.jpg&userId=2483773 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_7.jpg&userId=2483773 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_8.jpg&userId=2483773 [9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_9.jpg&userId=2483773 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_10.jpg&userId=2483773 [11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_11.jpg&userId=2483773 [12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_12.jpg&userId=2483773 [13]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_13.jpg&userId=2483773 [14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_14.jpg&userId=2483773 [15]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_15.jpg&userId=2483773 [16]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_16.jpg&userId=2483773 [17]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1700779780978-a2568bef-9e72-4f89-bfb7-ae5cc3ceb5b0_17.jpg&userId=2483773 Michele Nardelli 2023-11-23T23:11:49Z https://community.wolfram.com/groups/-/m/t/3000913 The number of Step-by-Step explanations in Wolfram|Alpha has been getting larger and larger. One of the latest step by step solutions we have been providing is the addition and subtraction of quantities. This includes working with quantities with different units of measurement, handling of decimal points and doing unit conversions. Let's look over at some of this new functionalities. Let's start with a straightforward example: the sums of 2 meters and 3 meters: ![enter image description here][1] ## Summing Quantities with Different Units of Measurements ## One of the most common issues that one encounters when summing physical quantities is summing quantities which have the same physical dimension (e.g., Length, Time, Mass) but different units of measurement, for example, such as feet and meters. Wolfram|Alpha provides steps for getting the result in any of the units that appears in the input. Are you summing meters and feet? We'll return a step-by-step solution for the end unit in meters and another with the end unit in feet. ![enter image description here][2] ![enter image description here][3] ## Decimal Quantities ## A lot of real world calculations requires working with quantities that have decimal and significant digits. Here for example we are subtracting 12 astronomical units to 3.5 parsecs: ![enter image description here][4] ## Sum and Subtraction of Multiple Quantities ## The step-by-step addition and subtraction of quantities can be extended to sum of more than two numbers! An example of this below. As you can see you can choose the result to be in any of the units appearing in the sum: ![enter image description here][5] ## Conclusion ## We hope this new functionality will help you when studying or for checking your calculations. Stay tuned for upcoming posts, such as exploring how to perform multiplication of quantities Step-by-Step. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-08-24at18.01.23.png&userId=2940410 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-08-25at16.37.40.png&userId=2940410 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-08-25at16.37.58.png&userId=2940410 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-08-25at16.43.54.png&userId=2940410 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-08-25at16.50.29.png&userId=2940410 Daniele Ceravolo 2023-08-29T10:03:00Z https://community.wolfram.com/groups/-/m/t/2936605 instrucciones de wolfram Lorena Casillas 2023-06-12T23:37:00Z https://community.wolfram.com/groups/-/m/t/2840816 These are the so-called "recurring numbers", which result from analyzing various equations of that sector of mathematics studied by Srinivasa Ramanujan (Theory of Numbers) and various equations of various sectors of Theoretical Physics (String Theory) and of Theoretical Cosmology (Black Holes and cosmological inflation) ![enter image description here][1] ![enter image description here][2] ![enter image description here][3] ![enter image description here][4] ![enter image description here][5] ![enter image description here][6] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1270Immagine1.png&userId=2483773 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8411Immagine2.png&userId=2483773 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8715Immagine3.png&userId=2483773 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10443Immagine4.png&userId=2483773 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Immagine5.png&userId=2483773 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Immagine6.png&userId=2483773 Michele Nardelli 2023-02-28T12:18:16Z https://community.wolfram.com/groups/-/m/t/2823806 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ea736d97-ac0b-42f9-b87d-bc5902508eda Peter Burbery 2023-02-04T15:36:19Z https://community.wolfram.com/groups/-/m/t/2823601 This is a ChatGPT prompt so that it acts as a WolframAlpha input generator: > I want you to act as a WolframAlpha input generator, providing me > with questions and queries to input into WolframAlpha. Your responses > should be well-formed, complete, and formatted in a way that would > provide the most accurate and helpful results from WolframAlpha. The > answers should not include any explanations or additional information, > only the formatted query for WolframAlpha. Let's start with a simple > one, what is the population of Paris? Icy Toc 2023-02-03T20:49:42Z https://community.wolfram.com/groups/-/m/t/2771372 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/12acc62b-9fb8-47b3-b562-1ada678dd8dd Eliza Kishan 2023-01-09T18:44:51Z https://community.wolfram.com/groups/-/m/t/2472931 For numerical analysis calculations, it would be good to display the results of applying the numerical analysis functions built into Wolfram, such as NSolve, NIntegrate, and NSum. 지성 김 2022-02-16T11:57:53Z https://community.wolfram.com/groups/-/m/t/2424580 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/5a0934c7-8bde-49b1-b3d8-9849b45c2163 Daniel Carvalho 2021-12-14T17:32:31Z