Solving a nice floor equation for integers

We solve the equation: floor(x/4)+floor(x/2)=27 for integer x.

#math,#algebra,#equation,numbers,integration,differentiation,derivative,integral,math elite,mathelite,maths,mathematics,calculus

[MathElite]

Please subscribe and click on the bell icon for more math content
Appreciate the support :DDD

[mathevengers]

Floor problems are always interesting.

[arshsverma]

I just found a pretty interesting fact
prod_(r=0)^(x-1) (1+cos((2r+1)pi/(2x))) = 2^(1-x)

[abhijeetraut]

I love floor/ceil questions, and this was beautifully solved

[math]

yeah, this one was nice, great job solving

[akshatjangra]

Hi! This video is cool, and I like seeing this computation that I dont think I’ve seen before. The golden ratio is tightly tied to the Fibonacci numbers, and I’ve seen some equations showing this but I don’t think I’ve seen this one.

It’a a little difficult to understand though. You go very quickly without stopping to say when things are important. You tell us how to go from one equation to the next without showing us. You ask us to compare equations without showing them side by side. You say phi instead of pi a lot. I’m fact, I’m not really sure why ei pi is in the equation at all.

I’d suggest you think a little harder about who your audience is and what they need to see. Spend a little more time on the punchlines, both the end punchline and the mini-punchlines a long the way. Either talk about the Fibonacci numbers like I know what they are and need a refresher, or like I don’t know what they are at all. Think about when they should be mentioned — do you want a big reveal, or should I be thinking about them from the start? Both are valid.

Also, maybe something interesting to think about, but the Fibonacci numbers ARE defined for negative integers! You can run the recurrence backwards and see that if F(0)=1 and F(1)=1, then you’d need F(-1)=0, then F(-2)=1, then F(-3)=-1, then F(-4)=2, and so on. See if you can find the pattern! It might be interesting to see if you can fit them into your pattern, too.

I like the video. I think it shows a cool math thing, and shows you care about cool math things. But people who care about cool math things tend to be bad at communicating them, at least at the start. Because it’s hard! It takes practice, and I hope this feedback helps you share your love of math with the world.

[p_square]

This is not to offend you neither to make you feel bad but your epsilon sign makes me really uncomfortable :)

[akshatjangra]

I uploaded your most beautiful equation on reddit and got this reply