Question

Can any one help ? I’m looking to fill the full wall with mirrors

Answer 1

This is a 7×7 grid of mirrors, meaning that each row and column has 8 dividing bars. This includes the bars between the outer mirrors and the wall, which appear to be thicker. I will first treat all bars as having the same thickness T cm. Let L and W be the length and width of each mirror in cm. Then we need

7L+8T=205

7W+8T=88

You actually have a degree of freedom here. You can pick the desired thickness, e.g., T=2. In that case we would have

7L+16=205 --> L=189/7=27

7W+16=88 --> W=72/7~10.28

To make this look exactly the same, you may wish to allow the outer bars to have a different width X. In that case your equations are

7L+6T+2X=205

7W+6T+2X=88

and you now get to pick T and X prior to solving. Hope it helps.

Answer 2

Given the allowed variability in the gap size, the easiest would be to use 1cm x 1cm mirrors.

Answer 3

Hello, thank you for participating in AskMath! I'm glad to help, but I'd advise you to use proper punctuation for your question, the text is confusing as it is. My understanding is that you want to fill the wall with perfectly square mirrors.

In brief, a good mirror size would be 26 cm. That way you can put 3 mirrors horizontally and 7 mirrors vertically, a total of 21 mirrors.

I think you would like to use more mirrors vertically because the wall is taller than it is wide. The ratio of these sizes is 205/88 = 2.33, which is roughly 7/3. So it would be interesting to use 7 mirrors vertically and 3 mirrors horizontally because the number of mirrors would try to match the shape of the wall.

To find the length of the mirror we have to sum the size of each mirror and the spacing between them, note that for 3 mirrors there is 4 spacings. let's call the mirror length L and the spacing lenth T.

3*L+4*T = 88 cm --> L = [ 88 - 4*T]/3

Assuming a spacing of 2 cm, the mirror size should be 26,67 cm, and a spacing of 3 cm is a mirror size of 3 cm --> 25,33 cm. So a mirror size between these values would give you a similar spacing. I choose 26 cm to get a nice round number. One important thing notice is that because we approximated the fraction at the start of the problem, the horizontal and vertical spacing will not be exactly the same, but should be close.

Feel free to ask if you have any further questions

Answer 4

You should probably think about how many mirrors you want next to eachother to fill those 88 centimetres. Doing that and the rest will fall into place. I would probably go with five. The reason being that more than that and they are too narrow. So, if you make them 16.4mm vide thatt adds up 82 cm. That gives you 1cm between mirrors and 1 cm from the edge of the walls.

For the width to height ratio I would go as close to the golden ratio, 1.618. If we go with 7 mirrors high, you can make them 28 cm tall. That way you can start 2 cm from the floor and have a 1 cm spacing between the mirrors.

How far from the floor do you want to start? There is sometimes not possible to start at the bottom as there may be something protruding from the wall there! If you tell me, I can adapt my calculations.


EDIT: Added more details.

Answer 5

Wait, aren't there mirrors already? Don't mind me but I can clearly see them in picture.