@dailymath94: The brachistochrone problem is one of those ideas that completely breaks your intuition. At first glance, the shortest path between two points is obviously a straight line—that’s basic geometry. But when gravity is involved and you’re trying to minimize time instead of distance, that instinct fails hard. The problem was famously posed in 1696 by Johann Bernoulli, and it asked: what curve allows an object to travel from one point to another in the least time under gravity, assuming no friction? Most people guessed straight lines or simple arcs. They were wrong. The surprising answer is a cycloid—the curve traced by a point on the rim of a rolling wheel. This result was independently derived by mathematical giants like Isaac Newton and Gottfried Wilhelm Leibniz, and it became one of the first major problems in the calculus of variations. Here’s the key idea: the fastest path is not about minimizing distance—it’s about optimizing speed over time. A straight line gives you the shortest route, but it doesn’t let you accelerate quickly. A cycloid, on the other hand, drops steeply at the start, letting gravity rapidly increase your speed. After that initial acceleration, the path flattens out, allowing you to carry that high velocity efficiently toward the endpoint. So even though the cycloid is longer than a straight line, you spend more time moving fast, which more than compensates for the extra distance. In contrast, the straight path keeps you slow for too long early on, and you never recover that lost time. This problem fundamentally reshaped how mathematicians think about optimization. It showed that the “best” solution depends entirely on what you’re optimizing for. Distance, time, energy—they all produce different answers. The brachistochrone is a brutal reminder that intuition alone is unreliable when systems involve change, accumulation, and trade-offs.#fyp #viral #math

∮ :

This is only for when there’s gravity

el_sigmamonkey :

Oh thats why planes go like this🤔

Cross :

My common sense not functioning..

Kris🫠 :

Once you start paying attention, people become very predictable, and that’s something I kept thinking about while reading a book called Virexon Cycle by Dalen Korvik, because the same emotions keep leading to the same outcomes..

Weird NoobGuest1 :

Why don't people apply this to running the 100 meter race

Krageon :

it doesn't optimize time, it optimizes energy

I eat Orbeez :

My dad taught me this when I was 6. We were skiing and he told me to go straight towards the lift. He followed the cycloid and traveled farther but got to the lift before me.

Maksthegymkid :

can you please explain more

Naully :

if the speed is constant, this won't work

Иисус :

straight line is shortest lol

AZdhaly :

LOOK AT REPOST

Mikkh 🏔 :

Intresting, but what if it's a light speed race? light has no mass, then, gravity won't work? it's mast be like "cycloid be second"?

Tacocat :

It doesn’t optimize time either, it optimizes for least action

𒉭samonyc𒉭 :

"it was the roundabout path that was the shortest, the shortest path was the roundabout"

Logan Reid :

. :

the faster way ist Not Always the better way

Anatole :

only one applies to gravity tho

PalletHitMe :

hey i did my math IA on this. It was not fun😭

E11 :

Scp 507 :

Isn’t the brachistochrone also just the shortest path? Because if you’re considering gravity, time, and space, you should probably just look at it through the lens of spacetime. And (I’m pretty sure) the brachistochrone is just the shortest path along the surface of the curved spacetime

Alex Jaeger :

When my calculus textbook started talking about cycloids and brachistochrones and tautochrones i kinda just shut my mind off

orr6hsarbew :

the Newton story about this is crazy

Mabye :

huh

LowTierLarp :

how do i larp this?

static🚙🇩🇲 :

Bs