Exploding triakis octahedron (short pyramids added on top of the faces) turning into an excavated octahedron (short pyramids dug into the faces) with pure #CSS #3D - live on @codepen: https://codepen.io/thebabydino/pen/DyrNrL
#Maths #geometry #polyhedra #css3D #cssTransform #cssTransforms #coding #code #transform #frontend #cssMaths #Sass #web #dev #webDevelopment #webDev #trigonometry #polyhedron #octahedron
One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe
A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.
#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS
#ThisWeeksFiddler, 20251212
This week the #puzzle is: Can You Topple the Tower? #geometry #trigonometry #CenterOfMass #integral A block tower consists of a solid rectangular prism whose height is 2 and whose base is a square of side length 1. A second prism, made of the same material, and with a base that’s L by 1 and a […]
https://stuff.ommadawn.dk/2025/12/16/thisweeksfiddler-20251212/
Later, on an walk through the woods, I realized that sine and cosine are their own fourth derivatives. This is not exactly news to mathematicians, but all of a sudden it was like OF COURSE they are! (3/n)
Most of the math I know beyond "business calculus" is math I picked up in grad school (economics) or taught myself later. I'm constantly reminded there are gaps in my knowledge. For example, trigonometry doesn't come up much in economics or statistics. (1/n)
Make A Cosine Wave Pattern
Cosine curves create elegant wave patterns cosine wave generates smooth horizontal oscillations creating mesmerizing visual Try it tonight
#python #pythontricks #codingtips #programmingtutorial #cosinewave #trigonometry #mathwaves #pythonmath #viralpython #pythonshorts #waveart
Problems In Mathematics With Hints And Solutions by V. Govorov; P. Dybov; N. Miroshin; S. Smirnova
The book contains more than three thousand mathematics problems and covers each topic taught at school. The problems were contributed by 120 of the higher schools of the USSR and all the universities.
The book is divided into, four parts: algebra and trigonometry, fundamentals of analysis, geometry and vector algebra, and the problems and questions set during oral examinations. The authors considered it necessary to include some material relating to complex numbers, combinatorics, the binomial theorem, elementary trigonometric inequalities, and set theory and the method of coordinates. The authors believe that this material will help the readers systematize their knowledge in the principal divisions of mathematics.
In writing the book, the authors have used their experience of examining students in mathematics at higher schools and the preparation of television courses designed to help students revise their knowledge for the entrance examinations to higher educational establishments.
To make it easier for readers to grasp the material, some of the sections have been supplemented with explanatory text. The problems are all answered and some have additional hints or complete solutions.
The more difficult problems are marked with asterisks. Part 4 is entitled “Oral Examination Problems and Questions” and includes samples suggested by the higher schools.
The authors hope that this book will help those who want to enter the various types of higher school, aid the teachers, and be of use to all those who want to deepen and systematize their knowledge of mathematics.
EDITED BY PROF. A.I. PRILEPKO, D.Sc.
Translated from the Russian by Irene Aleksanova
You can get the book here and here.
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Contents
Preface 5
Part 1 Algebra Trigonometry and Elementary Functions 9
1.1 Problems on Integers Criteria for Divisibility 9
1.2 Real Numbers Transformation of Algebraic Expressions 13
1.3 Mathematical Induction Elements of Combinatorics Binomial Theorem
1.4 Equations and Inequalities of the First and the Second Degree
1.5 Equations of Higher Degrees Rational Inequalities
1.6 Irrational Equations and Inequalities
1.7 Systems of Equations and Inequalities
1.8 The Domain of Definition and the Range of a Function
1.9 Exponential and Logarithmic Equations and Inequalities
1.10 Transformations of Trigonometric Expressions Inverse Trigonometric Functions
1.11 Solution of Trigonometric Equations Inequalities and Systems of Equations
1.12 Progressions
1.13 Solution of Problems on Derivation of Equations
1.14 Complex Numbers
Part 2 Fundamentals of Mathematical Analysis
2.1 Sequences and Their Limits An Infinitely Decreasing Geometric Progression Limits of Functions
2.2 The Derivative Investigating the Behaviour of Functions with the Aid of the Derivative
2.3 Graphs of Functions
2.4 The Antiderivative The Integral The Area of a Curvilinear Trapezoid
Part 3 Geometry and Vector Algebra
3.1 Vector Algebra
3.2 Plane Geometry Problems on Proof
3.3 Plane Geometry Construction Problems
3.4 Plane Geometry Calculation Problems
3.5 Solid Geometry Problems on Proof
3.6 Solid Geometry Calculation Problems
Part 4 Oral Examination Problems and Questions 241
4.1 Sample Examination Papers 241
4.2 Problems Set at an Oral Examination 244
Hints and Answers 265
Appendix 386
#algebra #geometry #mathematics #problemBooks #problemsAndSolutions #sovietLiterature #trigonometry
Ah yes, because nothing screams "basic #programming test" like dragging #trigonometry into a #game designed for kindergartners. 🤦♂️ Apparently, "if-else" wasn't enough of a brain teaser, so let's throw in some sine waves just to flex those over-engineering muscles. 🙃
https://susam.net/fizz-buzz-with-cosines.html #humor #overengineering #development #education #satire #HackerNews #ngated
#Noisevember! I ran out of time yesterday to post a track, so I'm posting two today. Here's one. It is again using a "direct" method: trig-filled code directly generates the sound. This one's nice and meditationy. Enjoy! https://soundcloud.com/matthew-m-conroy/direct-ii
#Noisevember! Another long-running project I have is one in which I try to make decent-sounding stuff using "direct" composition of the sound wave using simple code, generally with a lot (but not too many) trig functions. This is what I made today. It's pretty noisy despite for a waveform that is everywhere differentiable (aside from the discrete nature of digital sound, of course). I hope you enjoy it. https://soundcloud.com/matthew-m-conroy/direct
Math story time.
I tried to calculate the height of an antiprism and came up with this formula (x is 90° divided by the number of edges in the top and bottom polygons but that's not important here):
√(4 - 2 × (1 - cos(2x)) / sin(2x)²) / 2
I looked at MathWorld's version of the formula which seemed equivalent but was simpler:
√(1 - 1 / 4 / cos(x)²)
https://mathworld.wolfram.com/Antiprism.html
Then I was able to simplify my formula too:
√(4 - 2 × (1 - cos(2x)) / sin(2x)²) / 2
Replace cos(2x) with 1 - 2 × sin(x)²:
√(4 - 2 × (1 - (1 - 2 × sin(x)²)) / sin(2x)²) / 2
√(4 - 2 × (1 - 1 + 2 × sin(x)²) / sin(2x)²) / 2
√(4 - 4 × sin(x)² / sin(2x)²) / 2
√(4 × (1 - sin(x)² / sin(2x)²)) / 2
√(1 - sin(x)² / sin(2x)²)
√(1 - (sin(x) / sin(2x))²)
Replace sin(2x) with 2 × sin(x) × cos(x):
√(1 - (sin(x) / (2 × sin(x) × cos(x)))²)
√(1 - (sin(x) / 2 / sin(x) / cos(x))²)
√(1 - (1 / 2 / cos(x))²)
√(1 - 1 / 4 / cos(x)²)
There. (This took a few hours because I had to try many things and study more trigonometry.)
Did you know that the square of the sum of the sine of x and the cosine of x is actually the equivalent of the square of the sine of x plus the square of the cosine of x plus 2 multiplied by the product of the sine of x and the cosine of x? Because sin(x)^2+cos(x)^2=1, the function reduces to 1+2*sin(x)*cos(x). Furthermore, multiplying sin(x)*cos(x) by 2 is the equivalent of sin(2*x). #Trigonometry #Mathematics #Graphs
Hype for the Future 9B: Verfunctions in Trigonometry
The graph attached below showcases eight distinct and antiquated trigonometric functions regarding "versed" functions. Haversine in particular has historically been of importance in navigation, sailing, and perhaps even in communities such as fishing and whaling as well. From top to bottom, the functions listed in the legend correspond with the versine, vercosine, coversine, covercosine, haversine, havercosine, hacoversine, and hacovercosine, respectively.https://novatopflex.wordpress.com/2025/11/09/hype-for-the-future-9b-verfunctions-in-trigonometry/
#Inverse functions also exist using the #hyperbola in the role of the #circle. In these cases in #trigonometry the #arcfunctions are included below (possibly innocent errors about imaginary numbers):
#Inverse #functions in #trigonometry are included within the following image, using the #circle as the unit of measurement. #Mathematics also includes functions specifically about identifying the angles. All measurements are in #radians for each included graph.
I had saved that one a while back testing the meta VL model online (model forbidden in EU btw by Meta itself), let's see. #trigonometry
Next time? No next time. Next time someone sends something like 48/2(9+3) to me, pretending to be serious, I will say no because it is -ambiguous-. Problem solved!
If -serious- people have maths problem images, more like #trigonometry problems, that would be interesting, wouldn't it?
