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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.

11,985,284 次观看

“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

74,299 次观看

Rotation matrices at work.

Rotation matrices at work.

88,520 次观看

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

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

64,082 次观看

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

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

404,783 次观看

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 次观看

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 次观看

The Geometry of Integration by Parts.

The Geometry of Integration by Parts.

494,914 次观看

Unrolling Euler's Formula.

Unrolling Euler's Formula.

284,328 次观看

a³−b³ = (a−b)(a²+ab+b²)

a³−b³ = (a−b)(a²+ab+b²)

152,353 次观看

You Can Watch Euler's Formula, Unrolled.

You Can Watch Euler's Formula, Unrolled.

154,314 次观看

Rotation Matrices in Motion.

Rotation Matrices in Motion.

145,670 次观看

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

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

48,856 次观看

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 次观看

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 次观看

The Beautiful Gaussian Integral.

The Beautiful Gaussian Integral.

86,650 次观看

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 次观看

The Hidden Geometry of Trigonometric Functions and the Unit Circle.

The Hidden Geometry of Trigonometric Functions and the Unit Circle.

66,830 次观看

The difference between Δy/Δx and dy/dx.

The difference between Δy/Δx and dy/dx.

50,561 次观看

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 次观看

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The Fibonacci Spiral Clock.

The Fibonacci Spiral Clock.

131,907 次观看 • 1 天前

Fibonacci: From curves to cubes and back to curves.

Fibonacci: From curves to cubes and back to curves.

174,800 次观看 • 10 天前

“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

26,045 次观看 • 3 天前

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

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

67,633 次观看 • 9 天前

1³ + 2³ + … + n³ = (1 + 2 + … + n)²

1³ + 2³ + … + n³ = (1 + 2 + … + n)²

37,762 次观看 • 5 天前

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 次观看 • 7 天前

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

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

40,620 次观看 • 10 天前

Beauty is inseparable from mathematics...ᝰ.

Beauty is inseparable from mathematics...ᝰ.

114,076 次观看 • 1 个月前

All Six Trig Functions Are Just Lengths on One Circle.

All Six Trig Functions Are Just Lengths on One Circle.

239,043 次观看 • 2 个月前

You Can Watch Euler's Formula, Unrolled.

You Can Watch Euler's Formula, Unrolled.

154,314 次观看 • 1 个月前

The golden spiral, set in motion.

The golden spiral, set in motion.

85,124 次观看 • 1 个月前

Fractal Spirograph.

Fractal Spirograph.

127,630 次观看 • 1 个月前

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 次观看 • 10 天前

Mathematics. Functions. Dance.

Mathematics. Functions. Dance.

326,356 次观看 • 6 个月前

The Geometry of Perspective.

The Geometry of Perspective.

106,246 次观看 • 2 个月前

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 次观看 • 1 个月前

The Geometry Behind Trigonometry’s Most Famous Formula.

The Geometry Behind Trigonometry’s Most Famous Formula.

114,176 次观看 • 3 个月前

Every Curve Hiding Inside a Circle.

Every Curve Hiding Inside a Circle.

104,707 次观看 • 3 个月前

(𝑎 + 𝑏)³ = 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³

(𝑎 + 𝑏)³ = 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³

45,769 次观看 • 1 个月前

This is how a circle produces sine and cosine waves.

This is how a circle produces sine and cosine waves.

98,726 次观看 • 3 个月前