How do you create a perfect sphere?

[Xyooj]

the formula for the surface area of a sphere is SA = 4 (pi) r², with pi = 22/7 and r = radius of the sphere.

for example the SA for Earth with a radius of 6,378 km is 510,065,600 km²

what would the radius be in order that for you to lay a grid of perfect square on the surface of the sphere?

 

[Vanadium 50]

There are no perfect spheres in nature.

 

[Xyooj]

but how do you create one?

 

[Vanadium 50]

You don't.

 

[phinds]

pi = 22/7

No, not really. Close but no cigar.

 

[leroyjenkens]

Here's the closest you'll probably get to a perfect sphere. The video has a lot of superfluous, albeit interesting information. How the sphere is made is in the video around the middle.

https://www.youtube.com/watch?v=ZMByI4s-D-Y

 

[D H]

And even if you do manage to make a perfect sphere, you can't lay a grid of perfect squares on it. Squares live on planes, not spherical surfaces.

 

[DevilsAvocado]

the formula for the surface area of a sphere is SA = 4 (pi) r², with pi = 22/7 and r = radius of the sphere.

pi = 22/7 will not get you a “perfect sphere”, 21.991148575128552669238503682957/7 will get you closer.

for example the SA for Earth with a radius of 6,378 km is 510,065,600 km²

what would the radius be in order that for you to lay a grid of perfect square on the surface of the sphere?

How do you perfectly match a square on a circle? You are trying to do the impossible...
View attachment 162790

A square on the Euclidean plane has an internal angle of 90° at all four vertexes.
View attachment 162791

But when you apply a square on a sphere you get 120° internal angles.
View attachment 162792
This is not a “perfect square”...

You can use deltoidal icositetrahedron, but your “perfect squares” are lost again.

View attachment 194677

The best thing to do is triangulation, and high resolution on vertexes (=many). It will get you close, but never perfect.

View attachment 194678

 

[lisab]

To determine if a sphere is perfect, you need some way to measure it. That measuring device has some uncertainty associated with it (all such devices do). That means the uncertainty of the measuring device has to be greater than perfect. How is that possible? It isn't.

 

[krash661]

pi=-4*i*ln((-.5)^.5+.5^.5)

 

[DevilsAvocado]

That means the uncertainty of the measuring device has to be greater than perfect. How is that possible? It isn't.

Agree lisab, the only “perfect” certainty in nature is Heisenberg's uncertainty principle...

 

[dlgoff]

And even if you do manage to make a perfect sphere, you can't lay a grid of perfect squares on it. Squares live on planes, not spherical surfaces.

Even non-spherical shapes are not easy.

Although it was probably the most precisely figured mirror ever made, with variations from the prescribed curve of only 10 nanometers,^[24] at the perimeter it was too flat by about 2,200 nanometers (2.2 micrometres).^[54]

http://en.wikipedia.org/wiki/Hubble_Space_Telescope#Flawed_mirror

 

[Xyooj]

thanks everyone for helping :)

so even if the radius of sphere transforms pi (22/7) into a perfect number, i won't get a perfect sphere?

if the radius is 3500 km, the surface area would be 154,000,000 km2...these could be perfect square each measuring 1km on each of its four sides? so if i wrapped these into a sphere, some of you saying i cannot do so?

i was thinking of that whether on a curved plane or flat plane, if the grid defines perfect squares on these planes then whether you walk on the curved plane or flat plane the distance would be the same. but some of you said if i transform a flat plane into a curved plane, then the angle of the square changed?

 

[DevilsAvocado]

thanks everyone for helping :)

No worries mate

so even if the radius of sphere transforms pi (22/7) into a perfect number, i won't get a perfect sphere?

Nope, 7 x pi is not 22 but a “never ending mess of imperfection”...

if the radius is 3500 km, the surface area would be 154,000,000 km2...these could be perfect square each measuring 1km on each of its four sides? so if i wrapped these into a sphere, some of you saying i cannot do so?

Ever heard of polar bears and this guy??

And with 1 km² you will get trouble everywhere else too. See the bend in the water horizon in northern Wisconsin?

Trust me, same mess everywhere!

i was thinking of that whether on a curved plane or flat plane, if the grid defines perfect squares on these planes then whether you walk on the curved plane or flat plane the distance would be the same. but some of you said if i transform a flat plane into a curved plane, then the angle of the square changed?

Yup, the Euclidean plane does not work on spheres. However if you make your “perfect square” tiny, let’s say 1 cm², the ‘distortion’ is of course less. But you will never make a “perfect sphere” from “perfect squares”... impossible.

 

[daveyrocket]

If someone's definition of pi is 22/7, then maybe they don't have such strict criteria as to what constitutes a "perfect" sphere.

 

[Xyooj]

If someone's definition of pi is 22/7, then maybe they don't have such strict criteria as to what constitutes a "perfect" sphere.

could you please elaborate your version of "pi" ?
much appreciate the knowledge i could gain from you :)

 

[zoobyshoe]

could you please elaborate your version of "pi" ?
much appreciate the knowledge i could gain from you :)

22/7 goes wrong already in the third decimal place, which is why it's not a popular approximation. 3.14159...never goes wrong, it just never ends. It keeps getting closer and closer to pi without ever landing precisely on it.

When I worked in the machine shop we rounded pi off to 3.1416, which was as close as we ever had to be for any practical purpose. 22/7 or 3.1428, might easily have gotten us into a situation where parts didn't fit what they were supposed to fit.

 

[Xyooj]

22/7 goes wrong already in the third decimal place, which is why it's not a popular approximation. 3.14159...never goes wrong, it just never ends. It keeps getting closer and closer to pi without ever landing precisely on it.

When I worked in the machine shop we rounded pi off to 3.1416, which was as close as we ever had to be for any practical purpose. 22/7 or 3.1428, might easily have gotten us into a situation where parts didn't fit what they were supposed to fit.

thanks for sharing your shop experience, i just didn't realize that in our physical world that machines parts would need to be in the third digits or more after the decimal ...but good to know :)

the video of the si-28 sphere is interesting :)

 

[Xyooj]

if i have a ruler that measure 1m on a flat surface, if i bend it to measure a ball, the 1m does not change. or i lay a grid system with many perfect squares of each side being 1m on a flat surface, the length of the sides on these perfect squares will change their sides other than 1m each?

 

[Jonathan Scott]

if i have a ruler that measure 1m on a flat surface, if i bend it to measure a ball, the 1m does not change. or i lay a grid system with many perfect squares of each side being 1m on a flat surface, the length of the sides on these perfect squares will change their sides other than 1m each?

If you do that on a ball, a shape with four equal "straight" sides cannot have right angles at all four corners. If you try to force the corners to be right angles, the last corner will not meet.