26.2K
EESpherical coordinates with varying azimuth angle phi and polar angle theta.
@eeanimation
#Spherical Coordinates
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286.0K
THVolume of a Sphere: Spherical Coordination.
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#physics #science #fyp #amazing #explore
@thephysicist_boy
2.5K
BSSpherical coordinates v.s. Cartesian coordinates
@bsumathdept
107.5K
EXCoordinate Systems | Cartesian and Polar
Explore the fundamental connection between Cartesian and polar coordinates in this short video about coordinate systems. Discover how Cartesian coordinates, defined by horizontal (x) and vertical (y) distances, seamlessly relate to polar coordinates, represented by distance (r) from the origin and angle (θ) with respect to the horizontal axis.
Polar coordinates offer a different perspective on describing points in a plane compared to Cartesian coordinates. They’re particularly useful in scenarios where circular or rotational symmetry is involved, such as in physics, engineering, and mathematics.
One significant advantage of polar coordinates is their ability to simplify equations, especially those involving circular or radial patterns. For example, equations describing curves or shapes with rotational symmetry, like circles, ellipses, spirals, and sectors of circles, are often more straightforward in polar form.
#mathematics #math #maths
@explain.stuff
46.7K
THSpherical (r, φ, θ) to Cartesian (x, y, z):
x = r * cos(θ) * sin(φ)
y = r * sin(θ) * sin(φ)
z = r * cos(φ)
Cartesian (x, y, z) to Spherical (r, φ, θ):
r = √(x² + y² + z²)
φ = arccos(z / r)
θ = arctan(y / x)
These are spherical coordinates. They were used in part of this animation to calculate the spheres. Spherical coordinates define locations in space with three values. The distance from the center, called the radius, denoted by the letter r, the angle away from the north pole, or polar or zenith angle, denoted by the letter φ (“phi”), and the angle around the pole, call the azimuthal angle, denoted by the letter θ (“theta”). These three quantities can define any location in three-dimensional space.
Alternatively, rectilinear coordinates, or Cartesian coordinates, also define any location in three-dimensional space, but instead use the three quantities of x, y, and z, the distances in the right-left, forward-backwards, and up-down directions.
The equations above shows the relationship between the two coordinate systems, that is, if you have the three values from the one system, you can use these equations to find the three values in the other system.
If we are to truly awaken genius, we must see these equations as descriptions of a self-evident mathematical truth. Not simply memorize them, but learn to see them as descriptions of something we know. Can you see it?
This animation was created with the Java programming language in the Processing IDE (interactive development environment). Below you can see a snippet of code that uses spherical coordinates to generate the frames in this animation.
float theta = map(i, 0, n, 0, TAU);
float thetaStep = TAU / n;
float x = r * sin(phi) * cos(theta);
float y = r * sin(phi) * sin(theta);
float z = r * cos(phi);
AVector v = new AVector(x, y, z);
v.rotateY(rotatePhi);
v.rotateZ(rotateTheta);
#SphericalCoordinates #Mathematics #Enlightenment #Meditation #Education #Spirituality #Coding #ComputerScience #Love #Bhakti
@thebhaktimathguru
13.8K
STSpherical Coordinates #familyguy #computerscience #calc3
@stewie.cs
531.0K
MAPolar and Cartesian coordinates are two systems for locating points in a plane, each with its own advantages. In the Cartesian system, a point is described by its horizontal (x) and vertical (y) distances from the origin, forming a grid of perpendicular lines—ideal for straight-line motion and algebraic geometry. In contrast, the polar coordinate system locates points using a distance r from the origin and an angle θ from the positive x-axis. This system is especially useful for circular and spiral patterns, such as waves, planetary motion, or complex numbers. While Cartesian coordinates are best suited for linear relationships, polar coordinates excel in scenarios involving rotation, periodicity, or symmetry about a point.
I hope you like this video and follow @mathswithmuza for more!
#math #maths #learn #study #exam #foryou #fyp #algebra #calculus #reels #university #college #school #education #teaching #learning #new
@mathswithmuza
7.5K
THEver wondered how we actually calculate the volume of a sphere? 🌍
It’s more than just a formula you memorize. By using spherical coordinates, we can integrate through 3D space to find Volume.
Watch how these variables build the sphere from the ground up! 📐✨
#math #science #calculus #physics #stem
@thespinor
37.2K
EVSpherical coordinates! Link —> https://www.desmos.com/calculator/u16qa7cegl
#desmos #math
@evander941
103.9K
MAA sphere is one of the most perfectly balanced shapes in three-dimensional space. It is formed by all the points that are exactly the same distance from a central point, known as the center. This distance is called the radius. Because of this property, a sphere has no edges, corners, or flat surfaces—it is completely smooth and symmetrical in every direction. We can see spheres all around us in nature and everyday life, such as in planets, bubbles, and sports balls. Their roundness makes them efficient shapes, able to hold the greatest volume with the least surface area.
In mathematics and science, the sphere is used to model many real-world systems. It helps describe the shapes of stars and planets, the behavior of bubbles, and even the spread of light and sound from a single point. Its perfect symmetry makes it useful for studying geometry and physical laws that depend on distance and balance. Spheres also appear in higher-level math and physics as examples of objects with constant curvature, helping scientists understand more complex shapes and spaces.
Like this video and follow @mathswithmuza for more!
#math #maths #mathematics #physics #learn #learning #foryou #coding #ai #chatgpt #stem #education #manim #animation #school #surface #sphere #cool #fyp #reels #calculus #trigonometry #algebra
@mathswithmuza
175.0K
MA🌍 Have you ever wondered how we get the famous formula for the surface area of a sphere (4πR²)? 🤔
In this reel, I’ve visualized it in the most intuitive way — by imagining a sphere made of infinitely many thin circular rings, stacked smoothly from the bottom to the top. Each ring represents a tiny slice of the surface. Its circumference is given by 2πr, where the local radius r = R cos θ depends on the angle θ measured from the equator.
By summing up (integrating) all these circumferences from θ = −π/2 to π/2, we capture every part of the sphere’s curved surface. Through the power of integration, all these infinitesimal rings together reveal the elegant total area — 4πR² ✨
This method beautifully shows how geometry and calculus blend together — geometry gives shape, and calculus measures it.
If you love exploring visual math, calculus concepts, or just enjoy seeing how abstract formulas gain meaning through visualization, this reel is made for you! 🎥#math #fyp #likeme #studygram
@mathematisa
2.0K
CHA whole new world! #chemicalengineering #transportphenomena #cyllindricalcoordinates #sphericalcoordinates #momentumtransport
@chemicalengineeringguy
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