### Is there art in number?

## SquareCirclez Mathematics, learning, computing, travel - and whatever...

- Best Graphing Calculators for Studentsby Kathleen Cantor on November 2, 2021 at 3:50 am
While many students use calculators to perform basic calculations, others use them for more complex graphing functions. Graphing calculators are used in some sciences and math classes. Students must know which type of graphing calculator will best suit their particular needs. What to Look for In a Graphing Calculator A graphing calculator is an electronic The post Best Graphing Calculators for Students first appeared on SquareCirclez. Related posts: The Best Calculators for Geometry Out of all school supplies available to students, there is... SAT and ACT Calculators: TI-89 Plus Should you get a graphing calculator for the SATs? Absolutely.... Buyer’s Guide: TI-84 Graphing Calculator Math classes can be daunting. From a young age, I... How to Buy a Calculator A good calculator can be the difference between a great...

- The Best Calculators for Geometryby Kathleen Cantor on November 2, 2021 at 3:50 am
Out of all school supplies available to students, there is only one that we can always lean on when faced with challenging Mathematical problems. Calculators are one great invention that we are always grateful for in dealing with the different branches of mathematics such as algebra, trigonometry, and geometry. With these higher-level courses, there will The post The Best Calculators for Geometry first appeared on SquareCirclez. Related posts: Best Graphing Calculators for Students While many students use calculators to perform basic calculations, others... SAT and ACT Calculators: TI-89 Plus Should you get a graphing calculator for the SATs? Absolutely.... How to Buy a Calculator A good calculator can be the difference between a great... TI-83 Plus: The Math Exam Calculator The TI-83 series has been around for over 20 years,...

- A Rare Fibonacci Dayby Casey Allen on August 12, 2021 at 10:33 pm
Today is rather special. A day like today won't come around for almost another century. Today is rare and represents a “golden” opportunity for those in the know. Have you guessed it?? Well since you clicked on the title you already know the spoiler... Today, 8-13-21, combines three adjacent numbers in the Fibonacci Sequence. The The post A Rare Fibonacci Day first appeared on SquareCirclez. Related posts: Friday math movie - Nature by Numbers Here's a beautifully done video showing some of the math... Is Phi a Fibonacci furphy? Here's a debunking of some Phi and Fibonacci myths.... Fibonacci is alive and well - in AUD:SGD In this article we see an example of Fibonacci ratios... Friday math Movie - Math Rock and Fibonacci There are 2 movies this week. The first explains what...

- Best Middle School Back to School Math Suppliesby Kathleen Cantor on August 10, 2021 at 4:19 am
Your preteen probably has summer plans to sleep in, play video games, see friends, and maybe travel with family. It's the perfect time to relax and forget about the stress of school, homework, and math class, right? On the other hand, parents are practically giddy about sending their middle school students back to the classroom. The post Best Middle School Back to School Math Supplies first appeared on SquareCirclez. Related posts: Best High School Back-to-School Math Supplies Transitioning into high school is like entering the big leagues.... Homeschool Math Supplies Have you decided to homeschool your high school student this... Math Supplies: Math Manipulatives Teaching math is not always easy to do, even if... Teachers on a Budget: Essential Classroom Math Supplies Finding the balance between student success and personal spending in...

- Casio FX High Performance Calculatorby Kathleen Cantor on August 10, 2021 at 3:56 am
Check Lowest Price Casio FX calculators are well known for their quality and high performance. But if you want a Casio calculator that really earns its keep, the FX-991EX is as advanced as it can get. Between stellar features and the ability to use it in most regional and nationwide exams, like the SATs, it's The post Casio FX High Performance Calculator first appeared on SquareCirclez. Related posts: The billionth Casio calculator Casio's billionth calculator has been delivered. Where to next?... How to Buy a Calculator A good calculator can be the difference between a great... TI-83 Plus: The Math Exam Calculator The TI-83 series has been around for over 20 years,... TI-NSpire: The Most Powerful Calculator The TI-NSpire by Texas Instruments is arguably the most powerful...

## Recent Questions - Mathematics Stack Exchange most recent 30 from math.stackexchange.com

- Norm of $ \zeta_n^a + \zeta_n^{-a} - \zeta_n^b - \zeta_n^{-b} $.by Humourprince on January 24, 2022 at 6:28 am
Set $ \zeta_n = e^{2\pi i/n} $ as the $ n $-th root of unity. Consider the expression $$ z = \zeta_n^a + \zeta_n^{-a} - \zeta_n^b - \zeta_n^{-b} $$ where $ 0 < b < a < n $. I want to find the norm (i.e. the constant of its minimal polynomial) of $ z $. I have computed with Wolframalpha for few values of $ n $ and this is what I found: When $ n $ is prime, the norm is $ \pm n $, regardless of $ a, b $. When $ n = 2^k $, the norm is $ \pm 1, \pm 2, \pm 8 $. When $ n = p_1 ... p_m $, where $ p_i $ are prime, the norm is a multiple of some of the $ p_i $. Is there a known formula for this value? And how does it depend on $ a, b $?

- How to Solve 2x + 3y = 17by YellowMath on January 24, 2022 at 6:22 am
Is it really possible to solve an equation containing two variables, without another equation, if so, How do you solve it?

- Getting irrationally bound open sets from the rational basis producing the usual topology on $\mathbb{R}$by fine_structure on January 24, 2022 at 6:21 am
Self-studying Topology from Munkres, and in chapter 2, he mentions that the collection of open sets $$\mathcal{B} = \{\,(a,b) \mid a < b, a,b \in \mathbb{Q} \,\}$$ is a basis for $\mathbb{R}$ which produces the usual topology. I get the intuition behind this (I think) but how would one produce open sets like $(\sqrt{2}, \sqrt{3})$ from the above basis? We need to be able to get as close to $\sqrt{2}$ and $\sqrt{3}$ as possible. Do we have to specify a sequence in the rationals to get this? Is there a "nicer" way of being able to produce such an (irrationally bound) open set?

- Integer Optimization with boolean constraintsby fields1631 on January 24, 2022 at 6:20 am
everyone! I'm looking for an appropriate formulation of my problem (and a solver in Python). I have some integer variables, such as $a, b, c, ...$ I have to apply some constraints on them, such as $a == b$, and $(a > 0 \& b == 0) \| (a == 0 \& b > 0)$, and even $a \% 3 == b$. $a == b$ has already been supported by OR-Tools' CP-SAT solver, while others are not. My target to maximize would also been an expression with boolean parts, i.e., $(a > 0) + (b > 0) + ...$. This target is also unsupported. Could you help me convert the unsupported constraints and target into a supported style? I'm not sure whether it is possible.

- A functional equation problem.by Montasir Ahmed on January 24, 2022 at 6:17 am
I have found this functional equation problem in here https://gonitzoggo.com/archive/problem/423/english This problem states that, for function, $f:$$\mathbb{R}\rightarrow\mathbb{R}$ and $f(f(x))=x^2-x+1$ upon these given conditions, find the sum $f(1971)$+$f(50)$+$f(2021)$=? I've made some progress by setting $f(f(f(x)))=f(f(f(x)))$ $\Rightarrow f(x^2-x+1)$=$f(x)^2-f(x)+1$ Plugging in $x=1$, after solving the equation, $f(1)=f(1)^2-f(1)+1$ we find that, $f(1)=1$ As the equation's discriminant, $x^2-x+1$ is negative, so $f(x)\ge0 \;\forall x\in\mathbb{R}$ Also, I've found that, $f(0)=$ either $0$ or $1$ Can anyone help me to find the full solution for the problem ?

## Surrey Mathematics Research Blog The blog on research in mathematics at the University of Surrey

- Alessandro Torrielli gives virtual CPT Colloquium at Durham Universityby Tom Bridges on January 20, 2022 at 6:44 pm
The Department of Mathematical Sciences at Durham University hosted a talk by Alessandro Torrielli today (Thursday 20 January). The talk was in the Centre for Particle Theory Colloquium series, and the title of the talk was “Integrable scattering of massless particles and the AdS/CFT correspondence.” After a brief introduction to some of the impact which

- Ryan Poole passes PhD confirmation examinationby Tom Bridges on January 18, 2022 at 1:49 pm
Congratulations to Ryan Poole (shown in image left) for passing his PhD confirmation examination! It was held on Tuesday 18th January, and the examiners were Tom Bridges and Dave Lloyd. The title of Ryan’s project is “The effects of compliance on the stability of various flow configurations“. His project is supervised by Matt Turner with

- Paper of Daniele Farotti and Jan Gutowski published in Classical and Quantum Gravityby Tom Bridges on January 11, 2022 at 4:23 pm
The paper “Supersymmetry enhancement of heterotic horizons“, co-authored by Daniele Farotti and Jan Gutowski, has been published open access (link here) in the January 2022 issue of Classical and Quantum gravity. The paper considers the near horizon region of supersymmetric extremal black holes in ten-dimensional heterotic supergravity. It investigates the necessary and sufficient conditions for

- Anne Skeldon is co-author of a chapter in a major book on sleep medicineby Tom Bridges on January 11, 2022 at 2:12 pm
Anne Skeldon and Derk-Jan Dijk (Director, Surrey Sleep Research Centre) are co-authors of Chapter 38 of a major two volume book on “Principles and Practice of Sleep Medicine (Seventh Edition)”, published by Elsevier. The book has 2240 pages and 800 illustrations. Chapter 38 is entitled “Sleep homeostasis and models of sleep regulation.” A link to

- Paper of Sergey Zelik on inertial manifolds published in the SIAM J Math Analysisby Tom Bridges on January 7, 2022 at 5:36 pm
The paper “Inertial manifolds via spatial averaging revisited“, co-authored by Anna Kostianko (Imperial College London), Xinhua Li (Lanzhou University), Chunyou Sun (Lanzhou University), and Sergey Zelik, has been published in the SIAM Journal of Mathematical Analysis. The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial

## FlowingData Strength in Numbers

- How N95 masks workby Nathan Yau on January 21, 2022 at 5:31 pm
In efforts to reduce further spread of the virus, the US is set…Tags: coronavirus, mask, N95, Washington Post

- Joke machine learning projects to advance your careerby Nathan Yau on January 21, 2022 at 10:34 am
In an automated job climate that analyzes resumes and inspects social profiles, it…Tags: humor, Jess Peter, machine learning, Pudding

- ✚ Boring Charts – The Process 173by Nathan Yau on January 20, 2022 at 7:30 pm
Thinking about the differences between boring charts and not so boring charts.Tags: boring, whizbang

- Declining U.S. Birthsby Nathan Yau on January 20, 2022 at 12:27 pm
The number of births per month has been decreasing over the past decade. The pandemic seems to have sped up the process in the beginning.Tags: birth

- Death rates by vaccination booster statusby Nathan Yau on January 19, 2022 at 8:57 am
Our World in Data continues their important work on providing and showing up-to-date…Tags: coronavirus, mortality, Our World in Data, vaccination

## AnnMaria's Blog Words from the Prez

- Giving Students Their Money’s Worth Onlineby annmaria on August 23, 2020 at 6:26 am
As someone who has taught for over 30 years, and online for most of the last 7, I can tell you that online courses can actually be better.

- Tomorrow, I will be serious. Today, it’s quarantine clothesby annmaria on April 10, 2020 at 2:57 am
In my first ever post on fashion, I discuss rules for attire in web meetings. Number one: Wear clothes.

- The Blog Hourby annmaria on April 9, 2020 at 2:55 am
To fight off quarantine boredom, my granddaughter, Eva, and I have a nightly blogging challenge. Feel free to join us.

- Being (less) stressed during a pandemicby annmaria on April 8, 2020 at 2:51 am
Want to be stressed less? Start your day with something you look forward to and check out what your public library has to offer (yes, really)

- Everything is NOT just fineby annmaria on April 3, 2020 at 10:17 pm
If you think you should be feeling as if everything is fine, STOP IT! Everything is NOT fine. Even if you are healthy and your rent is paid, there is still a pandemic.

## Data & Society Data & Society advances public understanding of the social implications of data-centric technologies and automation.

- Data & Society Welcomes Ellen Pao & Raina Kumra to its Board of Directorsby veronica on January 11, 2022 at 3:00 pm
Data & Society is delighted to welcome Ellen Pao and Raina Kumra to our Board of Directors. Ellen Pao is a tech investor and advocate, the former CEO of reddit, and a cofounder of the award-winning diversity and inclusion nonprofit Project Include. Her writing has appeared in WIRED, The New York Times, The Washington Post,

- Recommendations for incorporating human rights into AI impact assessmentsby veronica on November 22, 2021 at 2:38 pm
Data & Society and the European Center for Not-for-Profit Law have collaborated to publish two papers with recommendations around human rights and algorithmic impact assessments. In the paper “Recommendations for Assessing AI Impacts to Human Rights, Democracy, and the Rule of Law,” our organizations emphasize that we are at a turning point for the future

- The Social Life of Algorithmic Harmsby veronica on October 28, 2021 at 8:21 pm
The AI on the Ground Initiative invites applications for Data & Society’s academic workshop, The Social Life of Algorithmic Harms. Our fundamental workshop question is: While the ways algorithmic systems interact with and inflect social life are theoretically boundless in their local contexts and trajectories, how can the harms they produce be practically organized in

- Postdoctoral Scholar Ranjit Singh To Receive CSCW 2021 Best Paper Awardby veronica on October 20, 2021 at 5:20 pm
Data & Society is pleased to share that our current Postdoctoral Scholar Ranjit Singh, along with his co-author Steven Jackson (Cornell University), will be awarded a CSCW 2021 Best Paper Award for “Seeing Like an Infrastructure: Low-resolution Citizens and the Aadhaar Identification Project,” to be officially presented later this month at the 24th ACM conference

- Parables of AI in/from the Global Southby chris on July 13, 2021 at 2:33 pm
On Thursday, October 21 and Friday, October 22, 2021, Data & Society Postdoctoral Scholar Ranjit Singh and Event Producer Rigoberto Lara Guzmán will host a two-day online workshop to reflect on storytelling both as a research craft and an intellectual practice. This will be an opportunity for collective listening and network building in the emerging

## MIT News - Data | Big data | Analytics | Statistics | IDSS | Operations research MIT news feed about: Data | Big data | Analytics | Statistics | IDSS | Operations research

- When should someone trust an AI assistant’s predictions?by Adam Zewe | MIT News Office on January 19, 2022 at 5:00 am
Researchers have created a method to help workers collaborate with artificial intelligence systems.

- The promise and pitfalls of artificial intelligence explored at TEDxMIT eventby Steve Nadis | MIT CSAIL on January 11, 2022 at 7:45 pm
MIT scientists discuss the future of AI with applications across many sectors, as a tool that can be both beneficial and harmful.

- Physics and the machine-learning “black box”by Mary Beth Gallagher | Department of Mechanical Engineering on January 10, 2022 at 8:15 pm
In 2.C01, George Barbastathis demonstrates how mechanical engineers can use their knowledge of physical systems to keep algorithms in check and develop more accurate predictions.

- Tackling hard computational problemsby Steve Nadis | Institute for Data, Systems, and Society on January 10, 2022 at 7:45 pm
David Gamarnik has developed a new tool, the overlap gap property, for understanding computational problems that appear intractable.

- Understanding air pollution from spaceby Julia C. Keller | School of Science on January 9, 2022 at 5:00 am
Arlene Fiore uses satellite data paired with ground observations to refine our understanding of ozone smog and interactions with meteorology and climate.

- Reducing food waste to increase access to affordable foodsby Zach Winn | MIT News Office on January 5, 2022 at 5:00 am
MIT alumni-founded Spoiler Alert matches major food brands with discount grocers to sell perishable products.

- Meet the 2021-22 Accenture Fellowsby Emma Foehringer Merchant | School of Engineering on January 4, 2022 at 6:40 pm
The 2021-22 Accenture Fellows are bolstering research and igniting ideas to help transform global business.

- Q&A: Cathy Wu on developing algorithms to safely integrate robots into our worldby Kim Martineau | MIT Schwarzman College of Computing on December 16, 2021 at 9:25 pm
Assistant professor of civil engineering describes her career in robotics as well as challenges and promises of human-robot interactions.

- Nonsense can make sense to machine-learning modelsby Rachel Gordon | MIT CSAIL on December 15, 2021 at 9:55 pm
Deep-learning methods confidently recognize images that are nonsense, a potential problem for medical and autonomous-driving decisions.

- Systems scientists find clues to why false news snowballs on social mediaby Adam Zewe | MIT News Office on December 15, 2021 at 5:00 am
A new model shows that the more polarized and hyperconnected a social network is, the more likely misinformation will spread.

## Mathematics – Wolfram Blog News, Views and Insights from Wolfram

- Learning Differential Equations in 10 Hours or Fewer with the Wolfram Languageby Luke Titus on January 19, 2022 at 3:00 pm
Differential equations are a cornerstone of modern mathematics. From quantum mechanics to population dynamics and stock market predictions, they play a crucial role in understanding the world around us. For this reason, courses on differential equations are core for many undergraduate degrees in the natural sciences, engineering and other fields. Today, I am proud to

- The Singular Euler–Maclaurin Expansion A New Twist to a Centuries-Old Problemby Andreas A. Buchheit on June 30, 2021 at 5:32 pm
Of all mathematical operations, addition is the most basic: It’s what we learn first in school. Historically, it is the most ancient. While the simple task of getting the sum of two numbers is simple, sums of many numbers can easily turn into a challenging numerical problem if the number of summands is very large.

- Is Your Function Continuous? Squaring Away the New Function Properties in the Wolfram Languageby Devendra Kapadia on March 30, 2021 at 8:17 pm
The Wolfram Language has several hundred built-in functions, ranging from sine to Heun. As a user, you can extend this collection in infinitely many ways by applying arithmetic operations and function composition. This could lead you to defining expressions of bewildering complexity, such as the following: ✕ f = SinhIntegral[ LogisticSigmoid[ ScorerHi[Tanh[AiryAi[HermiteH[-(1/2), x] - x

- 3D-Printed Jewelry Made with the Wolfram Language Showcases the Beauty of Mathematicsby Christopher Hanusa on February 15, 2021 at 8:09 pm
I enjoy turning mathematical concepts into wearable pieces of art. That’s the idea behind my business, Hanusa Design. I make unique products that feature striking designs inspired by the beauty and precision of mathematics. These pieces are created using the range of functionality in the Wolfram Language. Just in time for Valentine’s Day, we recently launched Spikey earrings in

- Step-by-Step Math Tools in Wolfram|Alpha Help Your Chemistry Course Prepby Becky Song on February 12, 2021 at 8:51 pm
Math is one of the main things that deters students from wanting to learn more about chemistry. Being a chemical engineering student, I understand this, especially for students who just have to get chemistry out of the way as a general education requirement. Essentially, step-by-step solutions are like your own on-demand math tutor: in addition

- How We Navigated a Hybrid Remote Learning Environment Using Wolfram Technologyby Timothy Newlin on January 14, 2021 at 6:00 pm
The past year of learning ushered in a variety of new experiences for instructors and students alike, and the United States Military Academy at West Point was no exception. In addition to masks in the classroom, reduced class sizes to allow for social distancing, rigorous testing and tracing efforts, and precautionary remote video classes, we

- New Wolfram Language Books on Wolfram|Alpha, Calculus, Applied Engineering and System Modelerby Paige Bremner on October 29, 2020 at 3:24 pm
The pandemic has postponed or canceled a lot of things this year, but luckily learning isn’t one of them. Check out these picks for new Wolfram Language books that will help you explore new software, calculus, engineering and more from the comfort of home. Hands-on Start to Wolfram|Alpha Notebook Edition New from Wolfram Media and

- Learn Linear Algebra in Five Hours Today with the Wolfram Language!by Devendra Kapadia on August 14, 2020 at 1:44 pm
Linear algebra is probably the easiest and the most useful branch of modern mathematics. Indeed, topics such as matrices and linear equations are often taught in middle or high school. On the other hand, concepts and techniques from linear algebra underlie cutting-edge disciplines such as data science and quantum computation. And in the field of

- New Wolfram Books: Releases from Wolfram Media and Others Featuring the Wolfram Languageby Wolfram Blog Team on July 2, 2020 at 6:11 pm
The first half of 2020 has brought with it another exciting batch of publications. Wolfram Media has released Conrad Wolfram’s The Math(s) Fix. Keep an eye out for the upcoming third edition of Hands-on Start to Wolfram Mathematica later in 2020. The Math(s) Fix The Math(s) Fix: An Education Blueprint for the AI Age is