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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.

Shorts

Solving a Rubik's Cube with graph theory.

Solving a Rubik's Cube with graph theory.

11,985,045 просмотров

“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 просмотров

Rotation matrices at work.

Rotation matrices at work.

88,520 просмотров

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

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

64,082 просмотров

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

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

404,783 просмотров

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 просмотров

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 просмотров

The Geometry of Integration by Parts.

The Geometry of Integration by Parts.

494,914 просмотров

Unrolling Euler's Formula.

Unrolling Euler's Formula.

284,328 просмотров

a³−b³ = (a−b)(a²+ab+b²)

a³−b³ = (a−b)(a²+ab+b²)

152,353 просмотров

You Can Watch Euler's Formula, Unrolled.

You Can Watch Euler's Formula, Unrolled.

154,314 просмотров

Rotation Matrices in Motion.

Rotation Matrices in Motion.

145,670 просмотров

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

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

48,856 просмотров

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 просмотров

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 просмотров

The Beautiful Gaussian Integral.

The Beautiful Gaussian Integral.

86,650 просмотров

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 просмотров

The Hidden Geometry of Trigonometric Functions and the Unit Circle.

The Hidden Geometry of Trigonometric Functions and the Unit Circle.

66,830 просмотров

The difference between Δy/Δx and dy/dx.

The difference between Δy/Δx and dy/dx.

50,561 просмотров

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 просмотров

Videos

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The Fibonacci Spiral Clock.

The Fibonacci Spiral Clock.

129,437 просмотров • 1 день назад

Fibonacci: From curves to cubes and back to curves.

Fibonacci: From curves to cubes and back to curves.

174,715 просмотров • 10 дней назад

“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 просмотров • 2 дней назад

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

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

67,633 просмотров • 8 дней назад

1³ + 2³ + … + n³ = (1 + 2 + … + n)²

1³ + 2³ + … + n³ = (1 + 2 + … + n)²

37,762 просмотров • 5 дней назад

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 просмотров • 7 дней назад

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

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

40,620 просмотров • 10 дней назад

Beauty is inseparable from mathematics...ᝰ.

Beauty is inseparable from mathematics...ᝰ.

114,076 просмотров • 1 месяц назад

All Six Trig Functions Are Just Lengths on One Circle.

All Six Trig Functions Are Just Lengths on One Circle.

239,043 просмотров • 2 месяцев назад

You Can Watch Euler's Formula, Unrolled.

You Can Watch Euler's Formula, Unrolled.

154,314 просмотров • 1 месяц назад

The golden spiral, set in motion.

The golden spiral, set in motion.

85,124 просмотров • 1 месяц назад

Fractal Spirograph.

Fractal Spirograph.

127,630 просмотров • 1 месяц назад

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 просмотров • 10 дней назад

Mathematics. Functions. Dance.

Mathematics. Functions. Dance.

326,356 просмотров • 6 месяцев назад

The Geometry of Perspective.

The Geometry of Perspective.

106,246 просмотров • 2 месяцев назад

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 просмотров • 1 месяц назад

The Geometry Behind Trigonometry’s Most Famous Formula.

The Geometry Behind Trigonometry’s Most Famous Formula.

114,176 просмотров • 3 месяцев назад

Every Curve Hiding Inside a Circle.

Every Curve Hiding Inside a Circle.

104,707 просмотров • 3 месяцев назад

(𝑎 + 𝑏)³ = 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³

(𝑎 + 𝑏)³ = 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³

45,769 просмотров • 1 месяц назад

This is how a circle produces sine and cosine waves.

This is how a circle produces sine and cosine waves.

98,726 просмотров • 3 месяцев назад