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A square, a marker and a piece of red string show why a path can look exactly like the diagonal and still be longer.
Zack D. Films
Story of No. 7 on the daily chartNo. 1 on the Science chart
Why this story? One of the most watched videos since yesterday, with 5,550,951 views.
How The Staircase Paradox Works 🤔
Draw a straight diagonal across a square. Then connect the same two corners with a staircase. Which route is shorter?
On paper, the answer is easy. The square's sides are marked 100mm, so the green diagonal comes to 141mm. The red staircase, stretched out as string, measures 200mm. Then the Short makes the steps smaller, and smaller again, until the staircase is almost impossible to tell apart from the diagonal.
Here is the catch the narrator spells out: "each stair step still goes sideways and then up." However tiny the steps get, they still add up to one full side across and one full side up. When both paths are peeled off the page and straightened, the staircase is still 200mm.
"How The Staircase Paradox Works 🤔" has drawn about 5.5 million views since yesterday. Its comment section has turned into an informal maths class. Viewers bring in limits and calculus, the coastline paradox and the old "proof" that pi equals 4. Others have their own running joke: Zack is now in his "paradox arc."
Published on Trari
Where next?
What viewers say
Zack in his paradox arc
@JunhuiZheng-i1xSee it on YouTubeThis is why mathematicians say length isn't always preserved when a shape is approached by a limit.
@Munkee_D_LuffySee it on YouTubeThis is the concept behind Coastline Paradox which explains that's its impossible to accurately measure the length of a country's coastline and the more precise the measurement the greater the length becomes to the point of infinity
@CossyMangoSee it on YouTube
5 more comments
Kinda reminds me of Flatland, about how the “circles” are actually shapes with sides so small and numerous that they’re practically indistinguishable from circles
@garg4531See it on YouTubeThis is how integration works too(calculus topic) its incredible too because we can literally jump into higher dimensions using integration.
@IraDosSantosSee it on YouTubeIts because each time the gap becomes smaller but it still covers more area than the other line so it will always be larger 😭
@ishakaushik6515See it on YouTubeThat's not a paradox, it's just normal physics.
Edit: Yes, it's math. But it's also physics in the sense that one line is already straight and the other is jagged. So of course if you straighten out the jagged line it will get longer! Physics.@frogpasteSee it on YouTubeZack has a lot of thoughts remaining
@lovegod9403See it on YouTube
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- Channel
- Zack D. Films
- Subscribers
- 29,600,000 ▲ 100,000 this week
- Channel views, last 7 days
- 780,388,567
- Channel views, pace per day
- 97,612,771 (on a normal day: 110,929,348)
- Video published
- November 7, 2026
- Video views so far
- 5,550,951 (less than a day online)
- Video views, pace per day
- 7,119,626
The numbers
This Short is one of the most watched new videos since yesterday, on a channel where a busy day is routine.
💡 Test your knowledge
Which theorem shows that a square's diagonal is about 1.41 times as long as its side?
For a right triangle, a² + b² = c², so a square with sides of 1 has a diagonal of √2, about 1.41.