## Recommended Posts

Even us metric users use tablespoons, teaspoons & cups.

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But they are defined in milliliters!

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Even furlongs can be defined in metric.

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The list of lengths of various countries' old miles makes for interesting reading, there being a spread of about a factor of three among various European miles.  I seem to recall that the Swedish mile was just about the longest, while the English (and old Roman) were towards the short end.

Nautical miles are something entirely different; those are one minute of arc (angle, not linear distance) along a great circle on or above (for aircraft) the surface of Earth.  Going from nautical miles to kilometers requires knowing how large the Earth is and (for precision) how its shape differs from a sphere.

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We still use the mil in daily live, defined as 10 km. The old definition, I think, was half a day's travel, the ideal separation between rest stops, inns and taverns.

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This video talks about the Roman mile, and a little bit of the history of roadside amenities.

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Gippsland teenager Mubasshir Murshed's parabola equation published in academic journal

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Question from today's quiz:

Bob and Doug are driving a sled through the frozen wastelands of the great white North. Bob drives the sled 4.95 km at a heading of 125°. Doug then takes over the driving and drives 7.17 km at a heading of 11°.  After Doug’s turn, how far are Bob and Doug from where they started, and in which direction?

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Are we permitted to assume that neither leg crossed the North Pole?

More precisely: is this assuming a Euclidean coordinate system on a flat plane, or are effects due to being near the coordinate singularity at the North Pole possibly important?

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20 hours ago, Cancer said:

Are we permitted to assume that neither leg crossed the North Pole?

More precisely: is this assuming a Euclidean coordinate system on a flat plane, or are effects due to being near the coordinate singularity at the North Pole possibly important?

We assume that the ground is perfectly flat, that the North Pole is infinitely far away, and that the sled travels in the absence of  ground friction and air resistance, like any sensible first-year high school physics class.

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Are there bears to consider?

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5 minutes ago, Pariah said:

We assume that the ground is perfectly flat, that the North Pole is infinitely far away, and that the sled travels in the absence of  ground friction and air resistance, like any sensible first-year high school physics class.

I didn’t know you were a flat earther.

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Only for the students who try to cheat.

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1 minute ago, Old Man said:

I didn’t know you were a flat earther.

Of course the Earth is flat...if you look at a small enough piece of it. You just have to know your limits.

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Actually the closer I look the less flat it gets. These atoms are really fluffy.

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Too close! Too close!!

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1 hour ago, Pariah said:

We assume that the ground is perfectly flat, that the North Pole is infinitely far away, and that the sled travels in the absence of  ground friction and air resistance, like any sensible first-year high school physics class.

For extra credit, do the geometry problem on the sphere, where the distance from the pole to any point in the travel might be comparable to or less than a one-leg travel distance.  Hint: you may need to know the radius of Earth to finish the problem.

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1 hour ago, Old Man said:

Actually the closer I look the less flat it gets. These atoms are really fluffy.

Go faster.  Then they flatten out fine.

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1 hour ago, L. Marcus said:

Are there bears to consider?

Are they spherical bears?

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Now you're asking about climate change, circumarctic ecology, and the health of apex predators.  Worthy questions, but probably those could wait a couple of weeks into the term.

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If Bob & Doug are travelling close to the speed of light then in the first leg of their trip they would be warping both time and space thus the 4.95 km is warped. The second leg of their journey doesn’t matter as Bob & Doug are energy.

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5 minutes ago, Bazza said:

Yeah, not getting involved in that Vietnam.

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Tell him to do a Socrates,* while explaining how Hegel makes biochemistry irrelevant.

EDIT: This quote also gets the point across.

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