prove-that-n-360-1-n-number-of-multiple-images-

Question Number 164821 by mathls last updated on 22/Jan/22

$${prove}\:{that}\:\:{n}=\frac{\mathrm{360}^{°} }{\propto}−\mathrm{1} \\ $$$${n}={number}\:{of}\:\:{multiple}\:{images}\: \\ $$

Commented by mathls last updated on 22/Jan/22

$${please}\:{i}\:{have}\:{problem}\:{and}\:{need}\:{to}\:{your} \\ $$$${help}. \\ $$

Commented by MJS_new last updated on 22/Jan/22

can you prove that c_0 =Π_(j=1) ^n x_j if you can′t, why?

$$\mathrm{can}\:\mathrm{you}\:\mathrm{prove}\:\mathrm{that}\:{c}_{\mathrm{0}} =\underset{{j}=\mathrm{1}} {\overset{{n}} {\prod}}{x}_{{j}} \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{can}'\mathrm{t},\:\mathrm{why}? \\ $$

Commented by mr W last updated on 23/Jan/22

the forum is not good place for such general or basic questions, just like how to prove E=mc^2 . Google is the right place to go, as i have suggested. but i guess you wont follow my suggestion.

$${the}\:{forum}\:{is}\:{not}\:{good}\:{place}\:{for}\:{such} \\ $$$${general}\:{or}\:{basic}\:\:{questions},\:{just}\:{like} \\ $$$${how}\:{to}\:{prove}\:{E}={mc}^{\mathrm{2}} .\:{Google}\:{is}\:{the} \\ $$$${right}\:{place}\:{to}\:{go},\:{as}\:{i}\:{have}\:{suggested}. \\ $$$${but}\:{i}\:{guess}\:{you}\:{wont}\:{follow}\:{my} \\ $$$${suggestion}. \\ $$

Commented by mathls last updated on 23/Jan/22

$${there}\:{is}\:{not}\:{the}\:{proof}\:{above}. \\ $$

Commented by mr W last updated on 24/Jan/22

i think it depends on what you think is a proof. i think you can also not find in google a “proof” for a(b+c)=ab+ac. it is easy to understand the number of multiple images in two adjacent mirrors with an angle θ between them. if θ divides 360°, then we can see that the whole circle (360°) can be divided into ((360°)/θ) equal parts. each part is the image of the others. we have thus totally ((360°)/θ) objects. since one object is the real object, the others are just the reflection of the reflection of the reflection etc. of the real object. that means the number of images is ((360°)/θ)−1. i know you wont think this is a proof.

$${i}\:{think}\:{it}\:{depends}\:{on}\:{what}\:{you}\:{think} \\ $$$${is}\:{a}\:{proof}.\:{i}\:{think}\:{you}\:{can}\:{also}\:{not} \\ $$$${find}\:{in}\:{google}\:{a}\:“{proof}''\:{for}\: \\ $$$${a}\left({b}+{c}\right)={ab}+{ac}. \\ $$$$ \\ $$$${it}\:{is}\:{easy}\:{to}\:{understand}\:{the}\:{number} \\ $$$${of}\:{multiple}\:{images}\:{in}\:{two}\:{adjacent} \\ $$$${mirrors}\:{with}\:{an}\:{angle}\:\theta\:{between}\:{them}. \\ $$$${if}\:\theta\:{divides}\:\mathrm{360}°,\:{then}\:{we}\:{can}\:{see}\:{that} \\ $$$${the}\:{whole}\:{circle}\:\left(\mathrm{360}°\right)\:{can}\:{be}\:{divided} \\ $$$${into}\:\frac{\mathrm{360}°}{\theta}\:{equal}\:{parts}.\:{each}\:{part}\:{is}\:{the} \\ $$$${image}\:{of}\:{the}\:{others}.\:{we}\:{have}\:{thus} \\ $$$${totally}\:\frac{\mathrm{360}°}{\theta}\:{objects}.\:{since}\:{one}\:{object} \\ $$$${is}\:{the}\:{real}\:{object},\:{the}\:{others}\:{are}\:{just} \\ $$$${the}\:{reflection}\:{of}\:{the}\:{reflection}\:{of} \\ $$$${the}\:{reflection}\:{etc}.\:{of}\:{the}\:{real}\:{object}. \\ $$$${that}\:{means}\:{the}\:{number}\:{of}\:{images} \\ $$$${is}\:\frac{\mathrm{360}°}{\theta}−\mathrm{1}.\:{i}\:{know}\:{you}\:{wont}\:{think}\: \\ $$$${this}\:{is}\:{a}\:{proof}. \\ $$

Commented by mr W last updated on 24/Jan/22