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That Pythagoras guy

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Wendell
(@wendell)
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Topic starter Posted : November 19, 2021 11:39 am
RPlumb314, Jitterboogie, Field Dog and 9 people liked
RADAR
(@dougie)
5,000+ posts Member

He wasn't right:

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Posted : November 19, 2021 2:59 pm
FL/GA
(@flga-2-2)
5,000+ posts Supporter

JOHN NOLTON
(@john-nolton)
200+ posts Member

@dougie  The famous brachistochrone problem first proposed by John Bernoulli in June of 1696.

Every one taking Calculus will have to solve this problem; IF not sooner.

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Posted : November 19, 2021 3:35 pm
Jitterboogie, RADAR, FL/GA and 1 people liked
holy cow
(@holy-cow)
10,000+ posts Member

The shortest and the fastest are two different questions.

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Posted : November 19, 2021 4:05 pm
Jitterboogie, dmyhill, RADAR and 4 people liked
Bill93
(@bill93)
5,000+ posts Member

@holy-cow 

Yes, Pythagoras did not consider speed, only distance.

And the fastest track depends on whether we have solid or hollow rolling balls, or something sliding with or without friction.

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Posted : November 19, 2021 4:24 pm
Jitterboogie, dmyhill, RADAR and 2 people liked

MathTeacher
(@mathteacher)
1,000+ posts Member

Around here, it's traffic that screws things up. When too many drivers clog up the hypotenuse, the legs become faster.

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Posted : November 19, 2021 6:01 pm
Brad Ott
(@brad-ott)
5,000+ posts Supporter
Posted by: @mathteacher

traffic ~ it would be helpful if more drivers looked at traffic situations in terms of fluid dynamics.

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Posted : November 20, 2021 7:20 am
oldpacer
(@oldpacer)
200+ posts Member

That's why they don't build sidewalks on college campuses until AFTER students have been there a year. Because, 'the shortest distance between two objects' is the path a college student takes between classes.

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Posted : November 20, 2021 7:35 am
Jitterboogie, Gary, Brad Ott and 1 people liked

Bill93
(@bill93)
5,000+ posts Member

It would be nice if more drivers paid attention to signs. There is an on-ramp I use frequently that narrows from 2 lanes to 1 just before the left lane of the ramp becomes the right lane of the main road.There are two signs telling you to merge left. I'd guess that a quarter of the people in the right lane just stay to the right all the way to the main road.

The problem is that sometimes someone passes me on my right just as they run out of lane and are forced over. One time I didn't see a guy coming up on my right in time to brake and give him room, and he missed my front corner by 3 feet as his lane went away.

I've facetiously threatened to go out there at 3 am and repaint the lines.

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Posted : November 20, 2021 7:49 am
holy cow
(@holy-cow)
10,000+ posts Member

My gripe is the thought that on divided highways with two lanes on either side of the divider, you are supposed to be in the right hand lane unless you are passing someone.  This is especially true when driving on stretches of road where there is no congested traffic.  I have yet to receive a ticket for driving in the left hand lane when the road is following a curve to the left then gradually moving to the right hand lane when approaching a curve to the right, effectively following the shortest course.

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Posted : November 20, 2021 8:48 am
BStrand
(@bstrand)
1,000+ posts Member

I've noticed Idahoans are pretty bad about lingering in the left lane for... ever.  I just passed a couple people on the right last night on the way back into town.  That's only my #2 gripe about the drivers in this state though, the #1 thing is EASILY the clowns that use the middle turn lane as a temporary parking lot/merge lane to make a left hand turn into busy traffic.  I've lived in several different states and I have never, ever seen people think this was a smart or legal thing to do until I got to Idaho.  And I can assure you it is illegal (in Idaho at least) because after nearly crashing from this stupidity a couple times I called the police and asked.  If you see someone do this, please chew their ass about the error of their way, and then feel free to give them a lesson on Pythagoreans too because it's a great bit of knowledge to have.

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Posted : November 20, 2021 9:06 am

Bill93
(@bill93)
5,000+ posts Member

@holy-cow 

Did you ever calculate how much distance or time you saved by that tactic?  Not much.

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Posted : November 20, 2021 9:18 am
RADAR liked
holy cow
(@holy-cow)
10,000+ posts Member

@bill93 

Way better than switching off lights to save on your electric bill.

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Posted : November 20, 2021 9:46 am
Bill93
(@bill93)
5,000+ posts Member
Posted by: @bill93

Did you ever calculate how much distance or time you saved by that tactic?  Not much.

You save by the difference in circumference of two circles having radii at each lane, times the fraction of a circle the curves make = 2*pi*(R1-R2)* delta/360.  .  If lanes are 12 ft wide and the curve has a delta of 45° (most highways don't have that much per curve) you save 3 ft, which at 70 mph is ~1/30 sec.

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Posted : November 20, 2021 10:41 am

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