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RICoordinate plane 101 🔢📊
Knowing the basics will get you far! #math #education
@richmathh
#Planimeter
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PIThis stunning visual represents an ellipse, one of the most fascinating shapes in mathematics. An ellipse is formed by the set of all points where the sum of distances from two fixed points (foci) remains constant. The animation shows how strings or lines stretched between these points create this smooth, symmetric curve — revealing the deep connection between geometry, harmony, and precision.
🌍 Practical Applications:
1. Planetary Orbits: The paths of planets around the Sun are elliptical, as described by Kepler’s Laws of Planetary Motion.
2. Reflective Properties: In an ellipse, any ray from one focus reflects to the other — used in whispering galleries, satellite dishes, and optical instruments.
3. Engineering & Design: Elliptical gears, tunnels, and domes use this shape for efficient force distribution.
4. Medical Imaging: MRI and ultrasound devices rely on elliptical paths of waves for accurate signal reflection.
5. Architecture & Acoustics: Elliptical rooms or ceilings help focus sound and light in specific areas for concert halls and theatres.
Follow @pi.mathematica for more interesting maths content & maths practical applications✨
#maths #mathusa #ellipses
@pi.mathematica
1.6K
VIWrapping 3D Space: Spherical Mapping Visualized
#topology #calculus #parameterspaceandphysicalspace #math #simulation
@visualx.anim
52.6K
NIThis is the charm of mathematics
@nikola_toyboy
795.0K
MAA Taylor approximation in 3D is a way to locally simplify a surface that depends on two inputs, like a height that changes with both x and y. Instead of working with the full surface, which might twist and curve in complicated ways, we approximate it near a chosen point using a simpler surface. The lowest level of approximation gives a flat plane that just touches the surface at that point, showing the immediate slope in different directions. Adding higher-order terms gently bends this plane, allowing it to mimic the surface’s curvature nearby. The closer you stay to the chosen point, the more accurate this simplified surface becomes.
From a visual perspective, Taylor approximations in 3D help us understand the local shape of a surface without needing to analyze the entire graph. The flat approximation explains how the surface initially rises or falls, while higher-order versions reveal whether it curves like a bowl, a ridge, or a saddle. This is especially useful in optimization, where decisions depend on local behavior rather than global complexity. Near important points, a complicated surface often behaves almost like a simple curved shape, making analysis and predictions much easier. In this way, a Taylor approximation becomes a geometric tool for seeing and understanding local structure in three dimensions.
Like and follow @mathswithmuza for more!
#math #3d #foryou #calculus #taylor
@mathswithmuza
276
11Every sine wave begins with a circle.#maths #instagood #viralvideos #viral #checkitout
@111v01s
558
AMPolar coordinates (r,θ) are essential for modeling systems with circular symmetry, rotation, or direction-based data. E.g. navigation 🧭, robotics, data analysis and modelling, nature & biology.
#geometry #naturelovers #math #graphics #desmos
@aman.kumar.3348
431
NOWho wins the accuracy race? Left vs. Right vs. Midpoint Riemann sums for int_0^pi sin(x) dx.
@not_abdo_benf
49.2M
SC90 degre clockwise rotation in the coordinate plane with a hole punch #geometry #transformations #visualmath #graphing
@scaffolded.math
18.1K
RUIf you don’t know your angles, you’re screwed for year 9 NAPLAN #study #exam #stem #studytips #math
@rubix_learning
201
IN📏 Converting inches to centimeters, feet to meters, or miles to kilometers?
This length converter makes it instant. Just pick your units, enter a number, and get precise results in seconds.
Perfect for travel, DIY projects, school, and everyday math
@inchcalculator
132
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