#algebra — Public Fediverse posts

Alright, future engineers!
**Factoring:** Breaking an expression into products of simpler terms.
Ex: `x^2 - 4 = (x-2)(x+2)`.
Pro-Tip: Always check for a GCF first! It simplifies everything.
#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!

**Quadratic Eq:** A polynomial equation where the highest power of the variable is 2.
Ex: `ax^2 + bx + c = 0`.
Pro-Tip: The Discriminant `(b^2-4ac)` reveals the number & type of roots (real/complex)!
#Algebra #Quadratics #STEM #StudyNotes

But wait, there's more! I also wrote a C++ program and Lua scripts to help you make animations of these higher-dimensional fractals. You can find these at https://codeberg.org/caten/RealAlgebraPlot

Not only can you see animations of the rock-paper-scissors fractal of central interest in my paper, you can also take slices of even higher-dimensional fractals coming from other real algebras, such as the octonions.

I wrote everything here from scratch as much as possible, so it has basically zero dependencies. I even opted to use Netpbm (https://en.wikipedia.org/wiki/Netpbm) so that I'd have an easy time writing image files directly without using a library. I am using #GraphicsMagick to produce animations. The same utility can be used to convert the output image files to a more familiar format like png.

#math #mathematics #algebra #analysis #ComplexAnalysis #fractals #Mandelbrot #MandelbrotSet #UniversalAlgebra #octonions #quaternions #cpp #Lua #LuaLang

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I'm extremely pleased to announce my newest paper is now available! In «A rock-paper-scissors Mandelbrot set» I study the analogue of the classic Mandelbrot set fractal over the 3-dimensional rock-paper-scissors algebra. This paper details a generalization of the methods of complex dynamics to arbitrary finite-dimensional real algebras. I found some surprising connections between the study of holomorphy in these algebras and their basic algebraic properties, as well as between the classic Mandelbrot set and its higher-dimensional cousins. This is my first foray into hypercomplex analysis, so it might come as a surprise if you've been following me, but over the past several months I thought it would do me some good to go back to my roots, zoom into some fractals, and play rock-paper-scissors. Here's the paper: https://aten.cool/documents/papers/A%20rock-paper-scissors%20Mandelbrot%20set%20[2026].pdf

#math #mathematics #algebra #analysis #ComplexAnalysis #academia #research #fractals #Mandelbrot #MandelbrotSet #UniversalAlgebra

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Alright, future engineers!
**Inverse Function:** Reverses another function, mapping its outputs back to inputs.
Ex: If f(x)=2x, then f^-1(x)=x/2.
Pro-Tip: Graphically, inverses reflect over y=x. Switch x & y to find them!
#Algebra #Functions #STEM #StudyNotes

Alright, future engineers!

**Factoring:** Breaking an expression into a product of simpler ones (its factors).
Ex: `x^2 - 4 = (x-2)(x+2)`.
Pro-Tip: Always look for a Greatest Common Factor (GCF) first! Simplifies everything.
#Algebra #MathSkills #STEM #StudyNotes

Alright, future engineers!
**Discriminant:** The `b^2 - 4ac` part of the quadratic formula, revealing the nature of its roots.
Ex: For `ax^2+bx+c=0`, `D = b^2 - 4ac`.
Pro-Tip: If D < 0, there are NO real solutions! Crucial for quick problem checks.
#Algebra #MathHacks #STEM #StudyNotes

Alright, future engineers!
**Logarithm:** The exponent to which a base must be raised to get a certain number.
Ex: `log_2(8) = 3` because `2^3 = 8`.
Pro-Tip: It's the *inverse* of exponentiation! Use properties like `log(A) + log(B) = log(AB)` to simplify equations.
#Algebra #MathHacks #STEM #StudyNotes

A SAT Attack on Tarski's High School Algebra Problem

https://arxiv.org/abs/2608.08421

Comments: https://news.ycombinator.com/item?id=49268565

#HackerNews #SAT #Attack #Tarski #Algebra #Problem #Mathematics #Education #Hacker #News

Alright, future engineers!
**Logarithms:** The inverse of exponentiation. They tell you what power a base needs to become a specific number.
Ex: `log_b(x) = y` is equivalent to `b^y = x`. So `log_2(8)=3` means `2^3=8`.
Pro-Tip: Use them to solve for variables *stuck in exponents*!
#Algebra #MathTips #STEM #StudyNotes

Alright, future engineers!
**Quadratic Formula:** Solves `ax^2+bx+c=0` for x.
Ex: `x = [-b +/- sqrt(b^2-4ac)] / 2a`
Pro-Tip: The discriminant `(b^2-4ac)` tells you if roots are real or complex & how many there are!
#Algebra #MathTips #STEM #StudyNotes

Alright, future engineers!
**Inverse Functions:** A function that undoes another function, effectively reversing its operation.
Ex: If `f(x)=2x+1`, its inverse `f^-1(x)=(x-1)/2`.
Pro-Tip: To find it, swap `x` and `y`, then solve for the new `y`!
#Algebra #Functions #STEM #StudyNotes

Alright, future engineers!
**Power Rule for Exponents:** To raise a power to another power, you multiply the exponents.
Ex: `(x^a)^b = x^(a*b)`. So, `(x^2)^3 = x^6`.
Pro-Tip: Don't confuse it with `x^a * x^b = x^(a+b)`! Totally different rules!
#Algebra #ExponentRules #STEM #StudyNotes

Niels Abel was born 224 years ago, on August 5, 1802. At just 21, he proved that no general algebraic formula can solve equations of degree 5, a problem that had challenged mathematicians for roughly 250 years.

Short on money, Abel paid the printer himself and condensed his proof into just six pages to keep costs down. He sent a copy to Gauss, but never received a response.

Abel died of tuberculosis at just 26. Two days later, a letter arrived announcing that he had been appointed professor in Berlin.

A breakthrough recognized too late.

#NielsAbel #Mathematics #MathHistory #HistoryOfMathematics #Mathematician #Algebra #AbstractAlgebra #QuinticEquation #Quintic #GaloisTheory #MathematicalHistory #MathFacts #ScienceHistory #STEMHistory #STEM #MathematicalBreakthrough #MathematicalGenius #Norway #NorwegianHistory #CarlFriedrichGauss #Equations #NumberTheory #PureMathematics #MathEducation #ScienceCommunication #OnThisDay #August5 #History #MathematicsLovers #MathTwitter

Alright, future engineers!
**Rational Expressions:** Fractions with polynomials in the numerator and/or denominator.
Ex: `(x^2 - 4) / (x + 2)`
Pro-Tip: Always factor first to simplify & identify values that make the denominator zero!
#Algebra #Simplify #STEM #StudyNotes

Alright, future engineers!
**Factoring Quadratics:** Expressing `ax^2 + bx + c` as a product of linear terms, often `(x-r1)(x-r2)`.
Ex: `x^2 + 7x + 10 = (x+2)(x+5)`
Pro-Tip: Look for two numbers that multiply to 'c' and add to 'b'. Simplifies finding roots!
#Algebra #MathSkills #STEM #StudyNotes

Meteorology

Current weather in Leonsberg SR SA with magnifico power of wttr.in & le passion grace beauty & colours of lolcat(6) 🏳️‍🌈 wttr curl(1) & {ba{c{k{z{fi}}}}}sh

Background photograph is the magenta Sunset at Waterkant scene composed with FL {fluorescent} UV {ultra violet} CIRC_POL {circular polarizer} and filters stacked using Nikon prime hardware

log

$ curl -v wttr.in/leonsberg_suriname|lolcat
% Total % Received % Xferd Average Speed Time Time Time Current
Dload Upload Total Spent Left Speed
0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0* Host wttr.in:80 was resolved.

• IPv6: (none)
• IPv4: 5.9.243.187
• Trying 5.9.243.187:80...
• Connected to wttr.in (5.9.243.187) port 80
• using HTTP/1.x> GET /leonsberg_suriname HTTP/1.1> Host: wttr.in> User-Agent: curl/8.14.1> Accept: />
• Request completely sent off< HTTP/1.1 200 OK< Access-Control-Allow-Origin: *< Cache-Control: public, max-age=600< Content-Type: text/plain; charset=utf-8< Date: Sun, 09 Aug 2026 14:38:04 GMT< Transfer-Encoding: chunked< { [2583 bytes data]100 8632 0 8632 0 0 19056 0 --:--:-- --:--:-- --:--:-- 19097

• Connection #0 to host wttr.in left intact
  Weather report: leonsberg_suriname

  \ / Sunny
  .-. +30(32) °C
  ― ( ) ― ← 11 km/h
  `-’ 10 km
  / \ 0.0 mm

Location: Leonsberg, Blauwgrond, Suriname [5.8692506,-55.1026346]

Note:

Remember to repeat the request with an interval of 8 then 24 secs when the server sends and empty response to curl, watch the LOG!

API

https://wttr.in

https://en.wikipedia.org/wiki/Bash_(Unix_shell)

https://gnu.org

https://directory.fsf.org/wiki/Bash

https://curl.se/

https://github.com/busyloop/lolcat

Z

#Weather #wttr #lolcat #curl #bash #csk #ksh #zsh #sh #fish #meteorology #environment #Physics #Chemistry #Mathematics #Lineair #algebra #technology #OpenSource #programming #POSIX

Alright, future engineers!
**Logarithms:** The exponent a base needs to become a number.
Ex: `log_2(8)=3` means `2^3=8`.
Pro-Tip: `log` IS the exponent! Essential for solving `x` in `b^x=N`.
#Algebra #MathTips #STEM #StudyNotes