Sum Cubes with Triangles This is a short, animated (wordless) visual proof demonstrating the sum of the first n positive cubes by rearranging triangular arrays into a larger triangular array. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! Here are four other visual proofs of sum of cubes formulas: https://youtu.be/YQLicI8R4Gs https://youtu.be/Ye9OPNqV9FA https://youtu.be/NxOcT_VKQR0 https://youtu.be/d1yM6Rq7Tfw This animation is based on a visual proof by Parames Laosinchai from the December 2012 issue of Mathematics Magazine (https://www.jstor.org/stable/10.4169/math.mag.85.5.360 page 360). To learn more about animating with manim, check out: https://manim.community #mathshorts #math #calculus #manim #proofwithoutwords visualproof - @mathvisualproofs

** ** ** ** You mean an “authoritative men’s outfit” to handle a _bad day_, right? 😎 So you still look firm + confident even when you’re in a _bad mood_, the key is: simple, neat, and neutral colors. An authoritative outfit = makes people instantly respect you. ### *3 Authoritative Men’s Outfit Formulas to Beat Bad Days* *1. Smart Casual CEO Mode* For college, work, or hanging out but still respected - *Top*: Plain Oxford shirt in navy, black, or white. Roll up the sleeves a bit. - *Bottoms*: Chino pants/ankle pants in khaki, charcoal, or black. No rips. - *Shoes*: Loafers, Chelsea boots, or clean white sneakers. - *Extra*: Leather/steel watch + sunglasses. *Vibes*: Calm but dominant. Bad day steps aside. *2. Monochrome Minimalist* The easiest but with a strong effect - *Top*: Black crew neck/henley T-shirt that fits the body, not oversized - *Bottoms*: Black dress pants or slim-fit black washed jeans - *Outer*: Overshirt or chore jacket in a matching color - *Shoes*: Boots or full black sneakers *Vibes*: Mysterious, focused, no drama. 3* Old Money Clean Look* Looks expensive without big logos - *Top*: Neat polo shirt or linen shirt in earth tones: olive, cream, mocha - *Bottoms*: Straight-cut dress pants in beige/off-white - *Shoes*: Premium white sneakers or penny loafers - *Extra*: Leather belt, slicked-back neat hair *Vibes*: Mature, classy, bad days don’t dare to bother you, ### *Key to Looking Authoritative So Bad Days Lose:* 1. *Fit is king*: Clothes that fit your body > expensive but oversized clothes 2. *Dark & neutral colors*: Black, navy, gray, olive = look firm 3. *Neat from head to toe*: Hair, nails, shoes clean. Messy = authority drops 4. *Don’t overdo accessories*: 1 watch is enough ### *Hashtag Edition* if you want to post OOTD when you’re in a bad day but still neat and authoritative: ` Want it made into a hangout, wedding reception, or campus version? Just tell me the event, I’ll mix and match the right one#BadDay #BerwibawaDuluBadDayKemudian #OutfitTagas #CleanLook #MenlnBlack

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piotrczarnota6 :

Sierpinski's triangle 👍

RJ :

Recently I tried to create a formula for it and I came up with 3((n(n+1))/2)

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