4.8K
GALet's craft the sum of these two vectors⛏
#vectoraddition
Background music: Minecraft - C418 🔥
More videos coming soon, hope these are helping 🫡
#vectors #minecraft
@garrymath_
#Vector Math
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NOWhich form of the equations do you like best? ⚡
Maxwell's equations describe the behaviour of electric and magnetic fields. They were originally written down by James Clerk Maxwell in 1861 as a set of 20 partial differential equations, but reformulated by Oliver Heaviside using vector calculus into four equations. The potential formulation reduced the number of equations to two, but they were still unwieldy. After Albert Einstein's discovery of special relativity in 1905, Hermann Minkowski quickly realized that matrices could be used to describe the electromagnetic field strength F, leading to the four-vector notation. Finally, Élie Cartan, using the language of differential geometry and differential forms, wrote the most compact form in 1924.
#physics #theoreticalphysics #electromagnetism #maxwell #calculus #math #animation #equations
@nonstandardmodels
723.8K
TO日本利用压电瓷砖将脚步转化为电能。这些瓷砖捕捉来自你脚步的动能。当你行走时，你的重量和动作会对瓷砖产生压力。瓷砖会轻微弯曲，从而产生机械应力。瓷砖内部的压电材料将这种应力转化为电能。每一步都会产生少量电荷，而数百万步结合在一起就能产生足够的电力来驱动 LED 灯、数字显示屏和传感器。在像涩谷车站这样繁忙的地方，每天大约有240万个脚步为这一系统作出贡献。这些电能可以被储存或立即使用，从而减少对传统电力来源的依赖，并支持可持续的城市基础设施。这种方法将日常运动转化为实用的可再生能源 #日本 #知识＃事实 ＃你知道吗 #推荐 #科技 #创新历史 技术实验热门
@topcommentexplosion
11.1K
ME✨ Eigenvectors and Matrices in 3D: The Direction That Never Changes ✨
In this animation, we explore how a matrix transforms space and what it really means for a vector to be an eigenvector.
🔹 Eigenvector: a special vector that, when the matrix is applied, does not change its direction, although its length can change. Algebraically:
Av=λv
Where:
v is the eigenvector.
λ is the eigenvalue, indicating how much the vector is scaled.
💡 This means the vector can stretch or shrink, but it always points in the same direction. If λ>1 it gets longer, if 0<λ<1 it shortens, and if λ<0 it flips and scales—but the line that defines its direction remains unchanged.
🔹 Geometric invariance: the direction of the vector is preserved, even if everything around it is transformed. In the animation, the red dashed line represents this invariant direction, showing the axis along which any multiple of the vector continues pointing the same way.
In the visualization:
The blue cube shows how the transformation matrix deforms space.
The yellow basis vectors show the original orientation of the space.
The red vector is the eigenvector: even as the matrix transforms everything else, it keeps its direction, highlighting the invariant axis of the system.
📊 Practical interpretation: eigenvectors and their associated eigenvalues are fundamental in physics, engineering, computer graphics, and system analysis. They reveal the “natural axes” of a linear system, the vibration modes of an object, or the directions of stretching and compression in a transformation.
In short: an eigenvector is like a compass in a sea of deformation, always pointing in the same direction no matter how everything around it changes.
#math #maths #physics #merlinomath #fisica
@merlinomaths
250.4K
MA✨ Discover the dynamic world of vector fields! Watch as arrows reveal the direction and magnitude of forces flowing through space, blending math and physics into a captivating visual journey. Every vector tells a story about how energy moves and interacts—dive in and see the beauty of mathematical motion! 🔄 #Math #Physics #VectorFields #Learning
✨ Découvrez le monde dynamique des champs vectoriels ! Observez comment les flèches illustrent la direction et la grandeur des forces qui circulent dans l’espace, mariant les mathématiques et la physique en une expérience visuelle fascinante. Chaque vecteur raconte une histoire sur le mouvement et l’interaction de l’énergie—plongez et admirez la beauté du mouvement mathématique ! 🔄 #Maths #Physique #ChampsVectoriels #Apprentissage
@maths_learning_._
3.6M
ONSanta explains vectors!
They're a lot easier than they seem and quite useful for lots of engineering projects 🔥
@onlocklearning
81.8K
AIWord embeddings are a way to represent words in a vector space, where each word is mapped to a high-dimensional vector. The key is that semantically similar words are represented by vectors that are close together in this space. This allows models to learn relationships such as synonyms or analogies.
One important aspect of word embeddings is how they incorporate position and directions to carry semantic meaning. While basic word embeddings capture the meaning of individual words, models such as Word2Vec learn to position words in such a way that not only the distance between vectors matters but also their direction.
C: @3blue1brown
Join our AI community for more posts like this @aibutsimple 🤖
#deeplearning #machinelearning #datascience #math #llm #transformer #gpt #education #mathematics #animation #computerscience #datascientist
@aibutsimple
268.1K
MAA vector field is a mathematical function that assigns a vector to every point in a space. Think of it like a map where, instead of just numbers or colors at each location, there’s an arrow showing direction and magnitude. For example, a weather map showing wind direction and speed at different points is a real-world example of a vector field. In more formal terms, if you’re in 2D or 3D space, a vector field takes each point (x, y) or (x, y, z) and assigns a vector that can describe things like velocity, force, or flow at that location.
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#education #mathematics #calculus #engineering #math #python #animation #science #physics #act #manim #jee #learn #code
@mathbythebeach
146.1K
EEVector algebra: addition
#math #engineering #physics #satisfying
@eeanimation
117.9K
THCross Product of Vectors
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#maths #mathematics #physics #iit #iitjee #animation
@thevisualmaths
10.8K
MAStruggling with vectors? Here's a quick tip
@mathswithisaac
195.8K
MAA vector field is a mathematical concept that assigns a vector (a quantity with both magnitude and direction) to each point in a space, like a plane or three-dimensional space. These fields are used to model physical phenomena such as fluid flow or gravitational forces, where a different force or velocity exists at every location. You can visualize a vector field as a collection of arrows, each representing the vector at a specific point, with the length of the arrow indicating the magnitude of the vector.
A parametric function (or set of parametric equations) describes a curve or surface where the coordinates (x, y, z, etc.) are expressed as functions of one or more independent variables called parameters. These parameters, often time (t), define how the coordinates change, allowing for the representation of curves, trajectories of moving points, and complex surfaces that might not be representable as a traditional function of y in terms of x.
The Fourier transform is a mathematical operation that converts a signal from the time or spatial domain into its constituent frequencies in the frequency domain, revealing the amplitude and phase of each frequency component within the original signal. This powerful tool is widely used by scientists and engineers for analyzing signals in various fields, including signal processing, telecommunications, image processing, and control systems, allowing them to decompose complex waveforms into simpler sinusoidal components.
A black hole is an astronomical body so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole.
Follow @mathvibes01, @mathematisa and @maths.empire for more 🔥 #math #manim #python #mathematics
@mathvibes01
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