Infinite 45 degree golden ratio thingy series related

In summary, The problem is to find the coordinate where an infinite amount of lines will end up, given that you start at (4,0) and continuously move at a 45 degree angle, with the distance traveled being divided by the square root of 2. The resulting movement creates a straight edged spiral, not a true spiral. Breaking it down into a sum of geometric series and treating the x and y motions separately may help in solving the problem.
  • #1
ebola_virus
14
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I've been trying to figure this problem out for hours on end and i can't even go on the tinernet to find the answer because its hard to search for. The problem is:
You start off at hte coordinate (4,0). you move up 45 degrees and the distance traveled is now divided by the square root of 2, hence 4/root2 = 2root2. This continious movement of 45 degrees results in a spiral much liekt he one in the golden ratio but just they're straight lines. the question asks what is the coordinate that the infinite amount of lines will end up in?
Does anyone know how to do this? Muc help is appreciatd.

because you move from (4,0) 45 degrees and the distance traveled is contiously divided by square root of 2, you end up landing at (6,2), then (6,4), then (5,5), then (5,4) and thus creating a straight edged spiral... they want to find the coordinate in which it ends up in. HELP!
 

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  • #2
? If each step is of the same length and at the end of each step you turn 45 degrees counter-clockwise, you are just moving around an octagon, not a spiral. After 8 steps, you are right back where you started.
 
  • #3
no no the distance traveled is divided by the square root of 2
 
  • #4
Interesting problem. I suggest you try breaking it down into a sum of geometric series. Treat the x and y motions seperately.
 
  • #5
ebola_virus said:
no no the distance traveled is divided by the square root of 2

You mean at each step, the distance is the previous distance divided by [tex]\frac{\sqrt{2}}{2}[/tex]?

Okay, I thought you just meant that the distance was the x and y components divided by [tex]\frac{\sqrt{2}}{2}[/tex] because of the 45 degree angle!
 

What is the "Infinite 45 degree golden ratio thingy series"?

The "Infinite 45 degree golden ratio thingy series" is a mathematical concept that involves a series of rectangles with sides in a 45 degree angle and a ratio of 1:1.618, which is known as the golden ratio. This series can continue infinitely, with each rectangle being half the size of the previous one.

How is the golden ratio related to the "Infinite 45 degree golden ratio thingy series"?

The golden ratio, also known as phi (φ), is the ratio between two quantities where the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. In the "Infinite 45 degree golden ratio thingy series", each rectangle is half the size of the previous one, resulting in a ratio of 1:1.618, which is the same as the golden ratio.

What is the significance of the "Infinite 45 degree golden ratio thingy series"?

The "Infinite 45 degree golden ratio thingy series" has significance in mathematics, art, and nature. It is considered aesthetically pleasing and has been used in architecture, design, and art throughout history. It also appears in natural phenomena, such as the arrangement of leaves on a stem or the spiral patterns of shells.

Can the "Infinite 45 degree golden ratio thingy series" be found in other shapes besides rectangles?

Yes, the "Infinite 45 degree golden ratio thingy series" can be found in other shapes, such as triangles, pentagons, and hexagons. As long as the shape has sides in a 45 degree angle and the ratio between the sides is 1:1.618, it can be a part of this series.

Is there a practical application for the "Infinite 45 degree golden ratio thingy series"?

While the "Infinite 45 degree golden ratio thingy series" may not have a direct practical application, it has been used in various fields, such as art, design, and architecture, to create aesthetically pleasing and harmonious compositions. It also serves as a reminder of the prevalence of the golden ratio in the world around us.

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