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The Math Flow

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Mathematics insights presented through animations, formulas, pictures, graphics, quotes, books, history, and memes. Open DM.

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Solving a Rubik's Cube with graph theory.

Solving a Rubik's Cube with graph theory.

11,985,045 görüntüleme

“Philosophy is written in this grand book, the universe, which stands continually open before our eyes… It is written in the language of mathematics.” - Galileo Galilei

“Philosophy is written in this grand book, the universe, which stands continually open before our eyes… It is written in the language of mathematics.” - Galileo Galilei

62,112 görüntüleme

Rotation matrices at work.

Rotation matrices at work.

88,520 görüntüleme

Pythagorean theorem, written on the unit circle: sin²θ + cos²θ = 1.

Pythagorean theorem, written on the unit circle: sin²θ + cos²θ = 1.

64,082 görüntüleme

(a + b + c)² = a² + b² + c² + 2(ab + ac + bc)

(a + b + c)² = a² + b² + c² + 2(ab + ac + bc)

404,783 görüntüleme

Sine and Cosine waves are...nothing but the shadows of a spinning circle.

Sine and Cosine waves are...nothing but the shadows of a spinning circle.

1,070,321 görüntüleme

Three golden rectangles, set mutually perpendicular, quietly define a regular icosahedron. Their twelve corners are exactly its twelve vertices.

Three golden rectangles, set mutually perpendicular, quietly define a regular icosahedron. Their twelve corners are exactly its twelve vertices.

26,351 görüntüleme

The Geometry of Integration by Parts.

The Geometry of Integration by Parts.

494,914 görüntüleme

Unrolling Euler's Formula.

Unrolling Euler's Formula.

284,328 görüntüleme

a³−b³ = (a−b)(a²+ab+b²)

a³−b³ = (a−b)(a²+ab+b²)

152,353 görüntüleme

You Can Watch Euler's Formula, Unrolled.

You Can Watch Euler's Formula, Unrolled.

154,314 görüntüleme

Rotation Matrices in Motion.

Rotation Matrices in Motion.

145,670 görüntüleme

A plane sliding through a double cone traces every conic section.

A plane sliding through a double cone traces every conic section.

48,856 görüntüleme

Viviani’s theorem demonstrates spatial conservation, showing that the three perpendicular lines behave like a zero-sum game: moving closer to one side requires corresponding movement away from the other two. Local changes maintain a global constant.

Viviani’s theorem demonstrates spatial conservation, showing that the three perpendicular lines behave like a zero-sum game: moving closer to one side requires corresponding movement away from the other two. Local changes maintain a global constant.

30,582 görüntüleme

At any point on a curve, there's one circle that fits the curve better than any other. It touches the curve at that point, leans in the same direction, and bends by the same amount. It tells you how sharply the curve is bending at that exact spot, and which way it's leaning. If the curve is bending sharply, the circle is small. If the curve is nearly straight, the circle is huge. The osculating circle of the curve.

At any point on a curve, there's one circle that fits the curve better than any other. It touches the curve at that point, leans in the same direction, and bends by the same amount. It tells you how sharply the curve is bending at that exact spot, and which way it's leaning. If the curve is bending sharply, the circle is small. If the curve is nearly straight, the circle is huge. The osculating circle of the curve.

51,256 görüntüleme

The Beautiful Gaussian Integral.

The Beautiful Gaussian Integral.

86,650 görüntüleme

The distance a circle travels in a single revolution without slipping equals π times its diameter, regardless of the wheel's size.

The distance a circle travels in a single revolution without slipping equals π times its diameter, regardless of the wheel's size.

28,118 görüntüleme

The Hidden Geometry of Trigonometric Functions and the Unit Circle.

The Hidden Geometry of Trigonometric Functions and the Unit Circle.

66,830 görüntüleme

The difference between Δy/Δx and dy/dx.

The difference between Δy/Δx and dy/dx.

50,561 görüntüleme

A square wave in time is a set of amplitudes in frequency, and the Fourier series is the bridge between the two.

A square wave in time is a set of amplitudes in frequency, and the Fourier series is the bridge between the two.

19,828 görüntüleme

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The Fibonacci Spiral Clock.

The Fibonacci Spiral Clock.

129,437 görüntüleme • 1 gün önce

Fibonacci: From curves to cubes and back to curves.

Fibonacci: From curves to cubes and back to curves.

174,715 görüntüleme • 10 gün önce

“The infinite! No other question has ever moved so profoundly the spirit of man.” - David Hilbert

“The infinite! No other question has ever moved so profoundly the spirit of man.” - David Hilbert

25,115 görüntüleme • 2 gün önce

"The eternal silence of these infinite spaces frightens me." - Blaise Pascal

"The eternal silence of these infinite spaces frightens me." - Blaise Pascal

67,633 görüntüleme • 8 gün önce

1³ + 2³ + … + n³ = (1 + 2 + … + n)²

1³ + 2³ + … + n³ = (1 + 2 + … + n)²

37,762 görüntüleme • 5 gün önce

The Aizawa attractor: It's a distinctive three-dimensional chaotic shape traced out by a system of three nonlinear differential equations with six parameters.

The Aizawa attractor: It's a distinctive three-dimensional chaotic shape traced out by a system of three nonlinear differential equations with six parameters.

41,676 görüntüleme • 7 gün önce

"The universe is written in the language of mathematics." – Galileo Galilei.

"The universe is written in the language of mathematics." – Galileo Galilei.

40,620 görüntüleme • 10 gün önce

Beauty is inseparable from mathematics...ᝰ.

Beauty is inseparable from mathematics...ᝰ.

114,076 görüntüleme • 1 ay önce

All Six Trig Functions Are Just Lengths on One Circle.

All Six Trig Functions Are Just Lengths on One Circle.

239,043 görüntüleme • 2 ay önce

You Can Watch Euler's Formula, Unrolled.

You Can Watch Euler's Formula, Unrolled.

154,314 görüntüleme • 1 ay önce

The golden spiral, set in motion.

The golden spiral, set in motion.

85,124 görüntüleme • 1 ay önce

Fractal Spirograph.

Fractal Spirograph.

127,630 görüntüleme • 1 ay önce

The Archimedean spiral is one of the oldest curves in mathematics, with turns that stay evenly spaced. Here, a straight line slowly turns into this spiral, and four hundred connected points follow its shape.

The Archimedean spiral is one of the oldest curves in mathematics, with turns that stay evenly spaced. Here, a straight line slowly turns into this spiral, and four hundred connected points follow its shape.

23,061 görüntüleme • 10 gün önce

Mathematics. Functions. Dance.

Mathematics. Functions. Dance.

326,356 görüntüleme • 6 ay önce

The Geometry of Perspective.

The Geometry of Perspective.

106,246 görüntüleme • 2 ay önce

Matrix multiplication seems complex until you observe it step by step. Watch how each of the nine entries is formed: one row from matrix A, one column from matrix B, three products, and one sum.

Matrix multiplication seems complex until you observe it step by step. Watch how each of the nine entries is formed: one row from matrix A, one column from matrix B, three products, and one sum.

43,661 görüntüleme • 1 ay önce

The Geometry Behind Trigonometry’s Most Famous Formula.

The Geometry Behind Trigonometry’s Most Famous Formula.

114,176 görüntüleme • 3 ay önce

Every Curve Hiding Inside a Circle.

Every Curve Hiding Inside a Circle.

104,707 görüntüleme • 3 ay önce

(𝑎 + 𝑏)³ = 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³

(𝑎 + 𝑏)³ = 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³

45,769 görüntüleme • 1 ay önce

This is how a circle produces sine and cosine waves.

This is how a circle produces sine and cosine waves.

98,726 görüntüleme • 3 ay önce