#Functions Sound

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When Equations Start to Sing - Ep. 1

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Trigonometry is the study of angles and triangles, but beneath the formulas lies something mesmerizing. Sine and cosine waves move in smooth, repeating patterns that look almost like a rhythmic dance. These curves power everything from sound waves and music to bridges, satellites, and even animation. What seems like abstract math is actually the hidden choreography behind motion, light, and rotation in the real world. Trigonometry isn’t just numbers — it’s the mathematics of patterns and movement. Now here’s something to think about: many people see trigonometry as difficult or boring. But is it actually boring, or is it just poorly visualized when taught? When you see the wave patterns moving, it feels more like art than arithmetic. " DM FOR CREDIT/ REMOVAL" #Trigonometry #MathIsBeautiful #SineWave #STEMReels #HiddenPatterns

Save this video for later if you happen to forget how to derive the formula for the integrating factor. 😅 Recall that an integrating factor is used to solve a first-order linear differential equation. In particular, if we multiply our differential equation by this integrating factor, we can then rewrite it into a form that's more amenable to integration as one side will simply be the derivative of a product. Anyway, I always try to show my students the origins of a formula whenever possible. That way, they're not just blindly using them. 😆 #math #maths #differential #equations #integral Background music: "Ultimate Comedy Music Vol. 10" by Sascha Ende (ende.app/en). Available for use under the CC BY 4.0 license (creativecommons.org/licenses/by/4.0/) at ENDE.APP.

The Upside-Down World of Math! (Arithmetic vs Harmonic Progression) 🙃🔢 ​ ​Have you ever tried turning a math problem completely upside down to solve it? 🙃 ​In Number Sequences, there is a secret mirror world. It is the difference between an Arithmetic Progression (AP) and a Harmonic Progression (HP). ​1. The Straight Line (Arithmetic Progression - AP) 📏 An AP is simple. You just keep adding the exact same number over and over. Think of walking up a staircase where every step is the exact same height. Example: 2, 4, 6, 8, 10... (We are just adding 2). ​2. The Upside-Down World (Harmonic Progression - HP) 🪞 An HP looks terrifying at first. The numbers get smaller and smaller, but not by the same amount. Example: 1/2, 1/4, 1/6, 1/8, 1/10... ​The Magic Connection: An HP is literally just an AP flipped upside down! (Mathematicians call this the Reciprocal). ​If you get a brutal test question about a Harmonic Progression, you do not need to learn a bunch of new, complicated formulas. All you do is: Step 1: Flip all the fractions upside down. Step 2: Solve it as an easy Arithmetic sequence. Step 3: Flip your final answer back upside down! ​The Zero Trap: ⚠️ There is exactly one rule in the Upside-Down world. An AP can have the number zero in it (like 3, 1, -1...), but an HP can NEVER have a zero! Why? Because if you try to flip zero upside down (1 divided by 0), you break the universe. The math is undefined! ​Follow @plotlab01 for more mind-blowing Number Theory & Math Tricks! ​Arithmetic Progression, Harmonic Progression, Number Sequences, AP vs HP, Reciprocals, Math Tricks, Algebra Formulas, Sequence and Series, Engineering Math, Divide by Zero, Math Visuals, Plotlab01. ​ ​#Algebra #MathTricks #NumberSequence #Engineering #Maths

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➡️Visualizing Japanese Multiplication of 210×5 ➡️ Follow @equationacademy for more #mathematics #multiplication #technology #fyp #science

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Area of a Circle: A Visual Proof Using a Triangle This animation visually proves the area of a circle by cutting it into equal sectors and rearranging them into a triangle-like shape. As the number of slices increases, the shape becomes smoother, revealing that the base corresponds to the circle’s circumference and the height corresponds to its radius. This simple rearrangement gives an intuitive, visual understanding of why the area of a circle works the way it does—no memorization, just geometry. #MathVisualized #CircleArea #VisualProof #Geometry #mathanimation