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Rotation Matrices in Motion.

Rotation Matrices in Motion.

114,532 Aufrufe

In 1963, mathematician Stanislaw Ulam got bored during a meeting and started doodling a grid spiral of sequential numbers. By highlighting only the primes, he uncovered what remains one of the most mesmerising visual mysteries in number theory: the Ulam Spiral.

In 1963, mathematician Stanislaw Ulam got bored during a meeting and started doodling a grid spiral of sequential numbers. By highlighting only the primes, he uncovered what remains one of the most mesmerising visual mysteries in number theory: the Ulam Spiral.

52,236 Aufrufe

The Beautiful Gaussian Integral.

The Beautiful Gaussian Integral.

60,295 Aufrufe

Anatomy of a Definite Integral.

Anatomy of a Definite Integral.

28,250 Aufrufe

a² - b² = (a+b)(a-b)

a² - b² = (a+b)(a-b)

40,740 Aufrufe

$We were taught the derivative as a formula to memorise. A definition to recite. A rule to apply. Something that "gives you the slope." But nobody told us what the formula was actually saying. Every symbol is a sentence. Every fraction is a question. Every limit is a story about getting closer and closer to something you can never quite touch. The top of the fraction? That's a change. A difference. A before and after. The bottom? That's how long you waited to see it. The limit? That's you, zooming in, refusing to settle for an approximation - chasing the truth all the way down to an interval so small it almost disappears. Put it all together, and you get the most honest question in calculus: How fast is something changing - right now, in this exact instant? Not on average. Not over a minute. Not eventually. Right now. That's it. That's the derivative. It's not a trick. It's not a rule. It's a beautifully precise way of asking a very human question: what's happening, in this moment? We spent years solving these. Maybe it's time we actually understood them.$

We were taught the derivative as a formula to memorise. A definition to recite. A rule to apply. Something that "gives you the slope." But nobody told us what the formula was actually saying. Every symbol is a sentence. Every fraction is a question. Every limit is a story about getting closer and closer to something you can never quite touch. The top of the fraction? That's a change. A difference. A before and after. The bottom? That's how long you waited to see it. The limit? That's you, zooming in, refusing to settle for an approximation - chasing the truth all the way down to an interval so small it almost disappears. Put it all together, and you get the most honest question in calculus: How fast is something changing - right now, in this exact instant? Not on average. Not over a minute. Not eventually. Right now. That's it. That's the derivative. It's not a trick. It's not a rule. It's a beautifully precise way of asking a very human question: what's happening, in this moment? We spent years solving these. Maybe it's time we actually understood them.

22,145 Aufrufe

The Basics of Electromagnetic Waves: Electricity and magnetism can sit still, like static electricity in your hair or a magnet stuck to your fridge. But when they move and change, they actually create each other. Together, they team up to form invisible ripples of energy called electromagnetic waves. Unlike ocean waves or sound waves, which need water or air to ripple through, electromagnetic waves don't need any material at all. They can easily travel through the completely empty vacuum of space. Maxwell's Big Idea: In the 1860s and 1870s, a Scottish scientist named James Clerk Maxwell figured out how this works. He wrote down the math showing exactly how electricity and magnetism link together to make these travelling waves. Today, scientists call his famous rules Maxwell's Equations. Hertz Proves It: Later, a German physicist named Heinrich Hertz took Maxwell's ideas and brought them to life. He was the first person to actually create and catch radio waves. To honour his work, we use the word hertz to measure how fast a wave vibrates (one cycle per second). Hertz's experiments proved two massive ideas: Radio waves are just invisible light: He showed that radio waves travel at the exact same speed as light, proving that they are actually a form of light we just can't see. Going wireless: He finally figured out how to detach these energy fields from physical wires, allowing the waves to fly freely through the air exactly as Maxwell had predicted.

The Basics of Electromagnetic Waves: Electricity and magnetism can sit still, like static electricity in your hair or a magnet stuck to your fridge. But when they move and change, they actually create each other. Together, they team up to form invisible ripples of energy called electromagnetic waves. Unlike ocean waves or sound waves, which need water or air to ripple through, electromagnetic waves don't need any material at all. They can easily travel through the completely empty vacuum of space. Maxwell's Big Idea: In the 1860s and 1870s, a Scottish scientist named James Clerk Maxwell figured out how this works. He wrote down the math showing exactly how electricity and magnetism link together to make these travelling waves. Today, scientists call his famous rules Maxwell's Equations. Hertz Proves It: Later, a German physicist named Heinrich Hertz took Maxwell's ideas and brought them to life. He was the first person to actually create and catch radio waves. To honour his work, we use the word hertz to measure how fast a wave vibrates (one cycle per second). Hertz's experiments proved two massive ideas: Radio waves are just invisible light: He showed that radio waves travel at the exact same speed as light, proving that they are actually a form of light we just can't see. Going wireless: He finally figured out how to detach these energy fields from physical wires, allowing the waves to fly freely through the air exactly as Maxwell had predicted.

36,982 Aufrufe

17 equations that changed the world.

17 equations that changed the world.

30,058 Aufrufe

Dynamics of the swing of a pendulum.

Dynamics of the swing of a pendulum.

19,973 Aufrufe

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Mathematics. Functions. Dance.

Mathematics. Functions. Dance.

309,748 Aufrufe • vor 1 Monat

The Unit Circle: Sines and Cosines in Motion

The Unit Circle: Sines and Cosines in Motion

69,376 Aufrufe • vor 21 Tagen

The Rössler Attractor.

The Rössler Attractor.

88,958 Aufrufe • vor 1 Monat

How the Unit Circle Generates Sine and Cosine Waves:👇

How the Unit Circle Generates Sine and Cosine Waves:👇

75,819 Aufrufe • vor 1 Monat

Calculation of the area under a curve.

Calculation of the area under a curve.

26,518 Aufrufe • vor 1 Monat

sin²x + cos²x =1

sin²x + cos²x =1

44,123 Aufrufe • vor 2 Monaten

Rössler Attractor: A system of three non-linear ordinary differential equations.

Rössler Attractor: A system of three non-linear ordinary differential equations.

39,008 Aufrufe • vor 1 Monat

Matrix Multiplication:👇

Matrix Multiplication:👇

38,687 Aufrufe • vor 2 Monaten

Unrolling circle into trigonometric functions.

Unrolling circle into trigonometric functions.

44,199 Aufrufe • vor 3 Monaten

Today, April 15, marks the 319th birthday of Leonhard Euler (1707–1783), arguably the most prolific mathematician ever to live.

Today, April 15, marks the 319th birthday of Leonhard Euler (1707–1783), arguably the most prolific mathematician ever to live.

24,474 Aufrufe • vor 1 Monat

The Lorenz attractor is the mathematical basis of the well-known "butterfly effect." It's derived from the Lorenz equations, a set of three ordinary differential equations developed as a simplified mathematical model for weather prediction.

The Lorenz attractor is the mathematical basis of the well-known "butterfly effect." It's derived from the Lorenz equations, a set of three ordinary differential equations developed as a simplified mathematical model for weather prediction.

20,894 Aufrufe • vor 1 Monat

Which is bigger: π^e or e^π?

Which is bigger: π^e or e^π?

33,638 Aufrufe • vor 3 Monaten

Visualizing 3x3 Matrix Multiplication.

Visualizing 3x3 Matrix Multiplication.

35,929 Aufrufe • vor 3 Monaten

Extracting the six trigonometric functions and their relationships from the unit circle.

Extracting the six trigonometric functions and their relationships from the unit circle.

25,598 Aufrufe • vor 2 Monaten

Deriving the quadratic formula.

Deriving the quadratic formula.

20,939 Aufrufe • vor 2 Monaten

The Geometry of a Derivative:👇

The Geometry of a Derivative:👇

18,712 Aufrufe • vor 2 Monaten

Taylor Series Expansion of eˣ.

Taylor Series Expansion of eˣ.

15,158 Aufrufe • vor 2 Monaten

17 Equations that changed the world.

17 Equations that changed the world.

18,804 Aufrufe • vor 3 Monaten

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