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

• Best Graphing Calculators for Students
by 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 Geometry
by 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 Day
by 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 Supplies
by 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 Calculator
by 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 = 17
by 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 constraints
by 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 University
by 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 examination
by 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 Gravity
by 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 medicine
by 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 Analysis
by 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

## 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 Directors
by 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 assessments
by 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 Harms
by 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 Award
by 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 South
by 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

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