[Tau]

What is x in this case and what are the units?

The post has been edited. I published it in pieces because I wasn't sure I was using the [tex] correctly and accidentally pressed post instead of preview.

[Rama Set]

Oh gotcha. Are the units Kms, miles, nautical miles?

[Tau]

The formula for the length of lines of longitude (in kilometers, because this is science) on the FE monopolar map is:

[Rama Set]

Bah!  Sorry about that.

[Tau]

Bah!  Sorry about that.

S'all good

I'm going through old threads looking for more math. I forgot how awful CT was.

[inquisitive]

Sydney to Santiago is 13 hours with Quantas.

[Tau]

Okay, someone posted this:



On the old forum as a distance formula, where d is the distance, r is latitude, theta is longitude, and subscripts denote the different places. I'm not sure if it's actually correct, though.

Sydney to Santiago is 13 hours with Quantas.

How is that relevant? This isn't a debate thread. Go bother us somewhere else.

[Tintagel]

Okay, someone posted this:



On the old forum as a distance formula, where d is the distance, r is latitude, theta is longitude, and subscripts denote the different places. I'm not sure if it's actually correct, though.

Looks like just an application of the Law of Cosines, which would make sense on the monopole map.  It's a good place to start at least.  Nice find, Tausami.

[Tau]

Thank you. I thought I recognized the formula, but geometry was a long time ago.

[Lord Dave]

Its simple trigonometry, Dave.

London is 0 degrees West/East. It is 51 degrees north.

Sydney is 151 degrees East and 33 degrees south.

Each degree is 60 nautical miles. Make a triangle.

angle 151 degrees. sides are (90-51) x 60) and ((90 x 60) +(33 x 60))

Bit of trig later


9,495 nautical miles. There is a fair bit of rounding on my part not using minutes etc but you see how its done. The round earth value is 9,174 nautical miles.

Hardly impossible to make a calculator, is it?

However, I don't want to generate all the answers. I'd rather the community got together and debated the calcs and the mathematics. This isn't Thork's flat earth society.

If a formula is arrived at, I'm sure me or Pizzaplanet can convert this to javascript or whatever their preference is.

Wouldn't the latitude and longitude lines be different on a flat earth due to the different positioning and elongation/shrinking of continents?

[Tau]

Its simple trigonometry, Dave.

London is 0 degrees West/East. It is 51 degrees north.

Sydney is 151 degrees East and 33 degrees south.

Each degree is 60 nautical miles. Make a triangle.

angle 151 degrees. sides are (90-51) x 60) and ((90 x 60) +(33 x 60))

Bit of trig later


9,495 nautical miles. There is a fair bit of rounding on my part not using minutes etc but you see how its done. The round earth value is 9,174 nautical miles.

Hardly impossible to make a calculator, is it?

However, I don't want to generate all the answers. I'd rather the community got together and debated the calcs and the mathematics. This isn't Thork's flat earth society.

If a formula is arrived at, I'm sure me or Pizzaplanet can convert this to javascript or whatever their preference is.

Wouldn't the latitude and longitude lines be different on a flat earth due to the different positioning and elongation/shrinking of continents?

Coordinates have nothing to do with topography, so no.

[Lord Dave]

Its simple trigonometry, Dave.

London is 0 degrees West/East. It is 51 degrees north.

Sydney is 151 degrees East and 33 degrees south.

Each degree is 60 nautical miles. Make a triangle.

angle 151 degrees. sides are (90-51) x 60) and ((90 x 60) +(33 x 60))

Bit of trig later


9,495 nautical miles. There is a fair bit of rounding on my part not using minutes etc but you see how its done. The round earth value is 9,174 nautical miles.

Hardly impossible to make a calculator, is it?

However, I don't want to generate all the answers. I'd rather the community got together and debated the calcs and the mathematics. This isn't Thork's flat earth society.

If a formula is arrived at, I'm sure me or Pizzaplanet can convert this to javascript or whatever their preference is.

Wouldn't the latitude and longitude lines be different on a flat earth due to the different positioning and elongation/shrinking of continents?

Coordinates have nothing to do with topography, so no.

It does when you try to fit the topography of a round earth onto a flat plane.  See map projections.

[Rama Set]

Its simple trigonometry, Dave.

London is 0 degrees West/East. It is 51 degrees north.

Sydney is 151 degrees East and 33 degrees south.

Each degree is 60 nautical miles. Make a triangle.

angle 151 degrees. sides are (90-51) x 60) and ((90 x 60) +(33 x 60))

Bit of trig later


9,495 nautical miles. There is a fair bit of rounding on my part not using minutes etc but you see how its done. The round earth value is 9,174 nautical miles.

Hardly impossible to make a calculator, is it?

However, I don't want to generate all the answers. I'd rather the community got together and debated the calcs and the mathematics. This isn't Thork's flat earth society.

If a formula is arrived at, I'm sure me or Pizzaplanet can convert this to javascript or whatever their preference is.

Wouldn't the latitude and longitude lines be different on a flat earth due to the different positioning and elongation/shrinking of continents?

Provided the Earth is a circle then they would only vary based on the diameter of the Earth since the system is defined by having 360 degrees of latitude and longitude.

[inquisitive]

Its simple trigonometry, Dave.

London is 0 degrees West/East. It is 51 degrees north.

Sydney is 151 degrees East and 33 degrees south.

Each degree is 60 nautical miles. Make a triangle.

angle 151 degrees. sides are (90-51) x 60) and ((90 x 60) +(33 x 60))

Bit of trig later


9,495 nautical miles. There is a fair bit of rounding on my part not using minutes etc but you see how its done. The round earth value is 9,174 nautical miles.

Hardly impossible to make a calculator, is it?

However, I don't want to generate all the answers. I'd rather the community got together and debated the calcs and the mathematics. This isn't Thork's flat earth society.

If a formula is arrived at, I'm sure me or Pizzaplanet can convert this to javascript or whatever their preference is.

Wouldn't the latitude and longitude lines be different on a flat earth due to the different positioning and elongation/shrinking of continents?

Provided the Earth is a circle then they would only vary based on the diameter of the Earth since the system is defined by having 360 degrees of latitude and longitude.

Flat earth distances must be different to round earth ones.

[Rama Set]

That would mean revamping their associated coordinates, not the coordinate system itself.

[Pete Svarrior]

Flat earth distances must be different to round earth ones.

Nope.

[inquisitive]

Flat earth distances must be different to round earth ones.

Nope.

Please explain why distances must be the same on different shaped surfaces.

[markjo]

Provided the Earth is a circle then they would only vary based on the diameter of the Earth since the system is defined by having 360 degrees of latitude and longitude.

Minor nit to pick: there are only 180 degrees of latitude.

[Rama Set]

Provided the Earth is a circle then they would only vary based on the diameter of the Earth since the system is defined by having 360 degrees of latitude and longitude.

Minor nit to pick: there are only 180 degrees of latitude.

So it is. But you do have to count each latitude twice to make a circumference effectively making 360 degrees to count.

[Pete Svarrior]

Please explain why distances must be the same on different shaped surfaces.

Why would I try explaining something I didn't say or claim? That'd be a silly thing for me to do, and it's a very silly thing for you to request.