#Math Notation

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A graph is a visual language of mathematics. From simple power functions like y = x², y = x³, up to y = x⁹, we observe how increasing the exponent changes curvature, symmetry, and growth rate. Even powers produce graphs symmetric about the y-axis, while odd powers preserve origin symmetry and change sign across quadrants. Trigonometric graphs such as sine and cosine introduce periodic behavior. Their wave-like structure models oscillation, phase, amplitude, and frequency—concepts essential in physics, engineering, and signal analysis. Through Taylor series, functions like sin(x), cos(x), and eˣ can be expressed as infinite polynomial sums. These series allow us to approximate smooth functions near a point using finite-degree polynomials, connecting algebra to calculus and numerical approximation. Parametric and implicit curves such as x³ + y³ = 1 through x⁹ + y⁹ = 1 reveal how altering exponents reshapes geometry, gradually transforming curvature and boundary behavior. These graphs are used in physics, engineering, computer science, economics, and even animations. 🚀 Understanding them makes math not just theory, but a tool for the real world. #reels #mathematics #likeme #fyp #trending

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“Mathematics is the language with which God has written the universe.” ~ Galileo Galilei. Video via: @5min__crafts . . #mathclass #muliplication #mathematics #math #numbers #maths #equation #ilovemath #mathisfun #matemáticas #matematicas #mathematical #mathteacher #mathlovers #solve #derivative #mathfun ⁦‪‬⁩#calculus #mathematical #mathlove

"The beauty of mathematics lies in its simplicity. It is like a delicate poem." — Bertrand Russell #math #mathematics #matematik

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🔹 Negative Determinant in 3D In linear algebra, a linear transformation f: V → V between vector spaces can be represented by a matrix once we fix an input basis B1 and an output basis B2. The notation M(f, B1, B2) denotes the matrix of f with respect to these bases. How is it built? Take each vector of the input basis B1 = {v1, v2, v3}. Compute its image: f(v1), f(v2), f(v3). Express each image in coordinates with respect to the output basis B2. Place these coordinate vectors as the columns of the matrix. So M(f, B1, B2) encodes, column by column, the coordinates of the images of the basis vectors of B1. If we use the same basis for both input and output (for example, the canonical basis B of R³), then M(f, B, B) directly tells us the transformed vectors in the same coordinate system. In the example we are visualizing: The vector e1 (the x-axis unit vector) remains unchanged. The vector e3 (the z-axis unit vector) also remains unchanged. The vector e2 (the y-axis unit vector) flips direction: from (0,1,0) to (0,−1,0). This creates a very typical situation: The parallelepiped generated by {f(e1), f(e2), f(e3)} has the same volume as that generated by {e1, e2, e3}. But the orientation changes: the cyclic order of the vectors no longer follows the right-hand rule, but instead the left-hand rule. 👉 The determinant captures exactly this: If det > 0, the orientation of the basis is preserved. If det < 0, the orientation is reversed. In this case, det(M(f,B,B)) < 0, which tells us the transformation preserves volume but flips orientation, just like a reflection in a mirror. #math #maths #physics #merlinomath