26.3K
EESpherical coordinates with varying azimuth angle phi and polar angle theta.
@eeanimation
#Spherical Coordinates
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608.5K
THVolume of a Sphere: Spherical Coordination.
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#physics #science #fyp #amazing #explore
@thephysicist_boy
14.1K
STSpherical Coordinates #familyguy #computerscience #calc3
@stewie.cs
2.5K
BSSpherical coordinates v.s. Cartesian coordinates
@bsumathdept
220.7K
PR🇧🇷 A visualização é sempre importante, as coordenadas esféricas sabem disso!
🇬🇧 Visualization is always important, spherical coordinates know that!
#math #university #spherical #coordinates #matematica #esfericas #calculus #calculo #fy
@professorjuliolombaldo
113.0K
PIThe surface area of a sphere is given by the formula 4πr² 📐✨. It’s derived by relating a sphere to a cylinder: if you unwrap the curved surface, it equals four times the area of a circle with the same radius. This elegant result shows how geometry connects shapes in surprising ways.
Follow (us) !! Boost Your Experience level Every Day ⚡ With - @pi.mathematica
#math #mathematics #time #knowledge #ideas #creative #facts #education #new #learning
@pi.mathematica
107.7K
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
7.9K
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
774.0K
ELA quick proof that the volume of a sphere is 4/3 * πr^3.
#math #calculus #geometry #proof #sphere
@electricalmath
7.6M
MAThis visual represents the unit circle, and how the value of the sine of theta varies as the angle theta increases. Sine of theta can be thought of as the y coordinate as we move along the unit circle. The reason for this is because the unit circle has a radius of 1 by definition, which is the hypotenuse of the right angled triangle. Now, as we move along the arc of the circle, starting from the coordinate (1,0), our x and y positions change. We can call the angle between the x axis and the hypotenuse theta, and by simple trigonometry we see that the y coordinate is always the sine of theta!
Follow @mathswithmuza for more…
#math #mathskills #mathproblems #trigonometry #sine #cosine #algebra #learn #calculus #school #foryou #fyp #why #how #university #college #stem #physics #coding #chatgpt #mathstricks #ai #foryoupage
@mathswithmuza
371.6K
MA✨ Master coordinate geometry with the Shoelace formula! ✨ Want to calculate the area of any polygon using just its coordinates? This game-changing method is perfect for students, math lovers, and competitive exam aspirants! 📚💡
Simply list your polygon’s coordinates: (x₁, y₁), (x₂, y₂), … (xₙ, yₙ), loop back to the first, multiply diagonals, subtract, and divide by 2 – bam, you’ve got the area! No complex integrals required. In this reel, I break down the Shoelace formula step-by-step, showing how it simplifies polygon area calculations for triangles, quadrilaterals, or any shape. 🌟
✅ Ideal for high school, BSc, or competitive exam preparation.
✅ Visual steps make coordinate geometry easy to grasp.
Tag a friend who needs this math hack! Save this reel for your next geometry. #fyp #likeme #views #studygram
What is the area of the Triangle ?
@mathematisa
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Instagram hosts thousands of posts under #Spherical Coordinates, creating one of the platform's most vibrant visual ecosystems. This massive collection represents trending moments, creative expressions, and global conversations happening right now.
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