kallend 1,625 #26 June 15, 2012 Quote Quote Quote OK here is a quick one. Imagine starting at a point on earth. Travel due south 10 miles. Travel due east 10 miles. Travel due north 10 miles. You are now back at the starting point. From how many starting points can this be done? Where is/are the point(s) located? (Assume the earth is a smooth sphere and there are no obstructions in your path.) a latitude with a 10 mile circumference either northern or southern hemisphere?? Close! the North Pole and any point along a latitude 10 miles north of the southern latitude with a 10 mile circumference! There are an infinite number of possibilities near (but more than 10 miles from the south pole). (You aren't restricted to one circuit around the pole, and you can start at any longitude).... The only sure way to survive a canopy collision is not to have one. Quote Share this post Link to post Share on other sites
kallend 1,625 #27 June 15, 2012 Related to the last question, how far from the south pole IS the point at which the circumference of the latitude line is exactly 10.00000 miles (in other words, you can't assume the Earth is flat)?... The only sure way to survive a canopy collision is not to have one. Quote Share this post Link to post Share on other sites
Niki1 1 #28 June 15, 2012 Quote Related to the last question, how far from the south pole IS the point at which the circumference of the latitude line is exactly 10.00000 miles (in other words, you can't assume the Earth is flat)? My quick answer is 3.1416... miles. but that's flat geometry. I bet calculus makes me wrong again. Or something else does.Most of the things worth doing in the world had been declared impossilbe before they were done. Louis D Brandeis Where are we going and why are we in this basket? Quote Share this post Link to post Share on other sites
muff528 3 #29 June 15, 2012 Quote Quote Quote Quote OK here is a quick one. Imagine starting at a point on earth. Travel due south 10 miles. Travel due east 10 miles. Travel due north 10 miles. You are now back at the starting point. From how many starting points can this be done? Where is/are the point(s) located? (Assume the earth is a smooth sphere and there are no obstructions in your path.) a latitude with a 10 mile circumference either northern or southern hemisphere?? Close! the North Pole and any point along a latitude 10 miles north of the southern latitude with a 10 mile circumference! There are an infinite number of possibilities near (but more than 10 miles from the south pole). (You aren't restricted to one circuit around the pole, and you can start at any longitude). Good one! I hadn't thought of making more than one lap!But, the question is "how many" starting points. If there are an infinite number of starting points (longitudes) at one latitude, then will/can adding more possibilities for starting latitudes increase the number of possible starting points? Doesn't infinite number = infinite number + some more? (I suppose you could try to divide the circumference of the starting latitude into planck units and call that the shortest divisible length thereby giving a finite number of start points ...but I'm not sure it works like that.) Quote Share this post Link to post Share on other sites
muff528 3 #30 June 15, 2012 Quote Quote Related to the last question, how far from the south pole IS the point at which the circumference of the latitude line is exactly 10.00000 miles (in other words, you can't assume the Earth is flat)? My quick answer is 3.1416... miles. but that's flat geometry. I bet calculus makes me wrong again. Or something else does. Half of that + a little. Quote Share this post Link to post Share on other sites
oldwomanc6 38 #31 June 15, 2012 Does anybody have a link to a visual model to show how the point(s) work near the the S.P.? I understand how it works at the N.P., but can't seem to wrap my head around how it would work down South. lisa WSCR 594 FB 1023 CBDB 9 Quote Share this post Link to post Share on other sites
muff528 3 #32 June 15, 2012 Quote Does anybody have a link to a visual model to show how the point(s) work near the the S.P.? I understand how it works at the N.P., but can't seem to wrap my head around how it would work down South. Quote Share this post Link to post Share on other sites
oldwomanc6 38 #33 June 15, 2012 Quote Quote Does anybody have a link to a visual model to show how the point(s) work near the the S.P.? I understand how it works at the N.P., but can't seem to wrap my head around how it would work down South. Thank you, it makes perfect sense now. lisa WSCR 594 FB 1023 CBDB 9 Quote Share this post Link to post Share on other sites
muff528 3 #34 June 15, 2012 Quote Quote Quote Quote Quote OK here is a quick one. Imagine starting at a point on earth. Travel due south 10 miles. Travel due east 10 miles. Travel due north 10 miles. You are now back at the starting point. From how many starting points can this be done? Where is/are the point(s) located? (Assume the earth is a smooth sphere and there are no obstructions in your path.) a latitude with a 10 mile circumference either northern or southern hemisphere?? Close! the North Pole and any point along a latitude 10 miles north of the southern latitude with a 10 mile circumference! There are an infinite number of possibilities near (but more than 10 miles from the south pole). (You aren't restricted to one circuit around the pole, and you can start at any longitude). Good one! I hadn't thought of making more than one lap!But, the question is "how many" starting points. If there are an infinite number of starting points (longitudes) at one latitude, then will/can adding more possibilities for starting latitudes increase the number of possible starting points? Doesn't infinite number = infinite number + some more? (I suppose you could try to divide the circumference of the starting latitude into planck units and call that the shortest divisible length thereby giving a finite number of start points ...but I'm not sure it works like that.) Well my original question does also ask "where". ..."quick thought" got me! Quote Share this post Link to post Share on other sites
rehmwa 2 #35 June 15, 2012 QuoteThere are an infinite number of possibilities near (but more than 10 miles from the south pole). (You aren't restricted to one circuit around the pole, and you can start at any longitude). not ANY latitude to start - they'd still have to be 10 miles north of specifically defined latitudes with circumferences of 10, 5, 2.5, 1,25, ...... but yes, any longitude on those starting latitudes and the north pole ... Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants Quote Share this post Link to post Share on other sites
rehmwa 2 #36 June 15, 2012 Quote Quote Quote Related to the last question, how far from the south pole IS the point at which the circumference of the latitude line is exactly 10.00000 miles (in other words, you can't assume the Earth is flat)? My quick answer is 3.1416... miles. but that's flat geometry. I bet calculus makes me wrong again. Or something else does. Half of that + a little. is the assumption a sphere? or an idealize oblate spheroid? or the actual planet's topography....? ... Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants Quote Share this post Link to post Share on other sites
rehmwa 2 #37 June 15, 2012 QuoteHere’s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost? here's a reword that is answerable or not depending on how you pause in the delivery of the question. A bat and ball cost a dollar and ten cents. How much does the ball cost? It's like the riddle - What crawls, is yellow, and can break a window? ... Driving is a one dimensional activity - a monkey can do it - being proud of your driving abilities is like being proud of being able to put on pants Quote Share this post Link to post Share on other sites
muff528 3 #38 June 15, 2012 QuoteQuoteThere are an infinite number of possibilities near (but more than 10 miles from the south pole). (You aren't restricted to one circuit around the pole, and you can start at any longitude). not ANY latitude to start - they'd still have to be 10 miles north of specifically defined latitudes with circumferences of 10, 5, 2.5, 1,25, ...... but yes, any longitude on those starting latitudes and the north pole Yes, but there are many multiple gazilliions of those starting latitudes as you approach the 10 mile distance (but not quite get there) from the pole. Quote Share this post Link to post Share on other sites
muff528 3 #39 June 15, 2012 Quote Quote Quote Quote Related to the last question, how far from the south pole IS the point at which the circumference of the latitude line is exactly 10.00000 miles (in other words, you can't assume the Earth is flat)? My quick answer is 3.1416... miles. but that's flat geometry. I bet calculus makes me wrong again. Or something else does. Half of that + a little. is the assumption a sphere? or an idealize oblate spheroid? or the actual planet's topography....? Doesn't matter. "half + a little" covers all 3 assumptions. Quote Share this post Link to post Share on other sites
kallend 1,625 #40 June 15, 2012 A Vogon galactic highway construction crew finds a small spherical rocky planet in its path and decides to bore (by vaporization) a cylindrical tunnel right through the center of the planet. Since they are paid piece rates, they have to measure the length of the resulting tunnel. It turns out to be exactly 1 Vogon mile in length. What is the volume of the remaining rock in the planet?... The only sure way to survive a canopy collision is not to have one. Quote Share this post Link to post Share on other sites
Squeak 17 #41 June 16, 2012 QuoteA Vogon galactic highway construction crew finds a small spherical rocky planet in its path and decides to bore (by vaporization) a cylindrical tunnel right through the center of the planet. Since they are paid piece rates, they have to measure the length of the resulting tunnel. It turns out to be exactly 1 Vogon mile in length. What is the volume of the remaining rock in the planet?42 cubic vogon milesYou are not now, nor will you ever be, good enough to not die in this sport (Sparky) My Life ROCKS! How's yours doing? Quote Share this post Link to post Share on other sites
oldwomanc6 38 #42 June 16, 2012 Quote A Vogon galactic highway construction crew finds a small spherical rocky planet in its path and decides to bore (by vaporization) a cylindrical tunnel right through the center of the planet. Since they are paid piece rates, they have to measure the length of the resulting tunnel. It turns out to be exactly 1 Vogon mile in length. What is the volume of the remaining rock in the planet? My first thought (quick) is that no volume measurement has been referenced, only length, so not enough info to possibly answer. Not a math major, just an artist . What do I know?lisa WSCR 594 FB 1023 CBDB 9 Quote Share this post Link to post Share on other sites
oldwomanc6 38 #43 June 16, 2012 42 I get it now! lisa WSCR 594 FB 1023 CBDB 9 Quote Share this post Link to post Share on other sites
muff528 3 #44 June 16, 2012 QuoteA Vogon galactic highway construction crew finds a small spherical rocky planet in its path and decides to bore (by vaporization) a cylindrical tunnel right through the center of the planet. Since they are paid piece rates, they have to measure the length of the resulting tunnel. It turns out to be exactly 1 Vogon mile in length. What is the volume of the remaining rock in the planet? Volume of the sphere - volume of the tunnel - the volume of the 2 "caps" (which are not included in the tunnel measurement). Don't I also need to know the diameter of the tunnel? Quote Share this post Link to post Share on other sites
JohnMitchell 14 #45 June 16, 2012 No, the answer if 42. I learned that while hitchhiking. Quote Share this post Link to post Share on other sites
muff528 3 #46 June 16, 2012 Quote No, the answer if 42. I learned that while hitchhiking. Quote Share this post Link to post Share on other sites
nanook 1 #47 June 16, 2012 my inebriated brain says "0". Don't know why. Seems like gravitational forces and the sudden loss of mass would cause some sort of disentigration._____________________________ "The trouble with quotes on the internet is that you can never know if they are genuine" - Abraham Lincoln Quote Share this post Link to post Share on other sites
kallend 1,625 #48 June 16, 2012 Quote Quote A Vogon galactic highway construction crew finds a small spherical rocky planet in its path and decides to bore (by vaporization) a cylindrical tunnel right through the center of the planet. Since they are paid piece rates, they have to measure the length of the resulting tunnel. It turns out to be exactly 1 Vogon mile in length. What is the volume of the remaining rock in the planet? My first thought (quick) is that no volume measurement has been referenced, only length, so not enough info to possibly answer. Not a math major, just an artist . What do I know? There is a unique answer, and knowing that helps solve the problem in your head in 30 seconds. Or you can use calculus and spend an hour over it.... The only sure way to survive a canopy collision is not to have one. Quote Share this post Link to post Share on other sites
muff528 3 #49 June 16, 2012 Quote Quote Quote A Vogon galactic highway construction crew finds a small spherical rocky planet in its path and decides to bore (by vaporization) a cylindrical tunnel right through the center of the planet. Since they are paid piece rates, they have to measure the length of the resulting tunnel. It turns out to be exactly 1 Vogon mile in length. What is the volume of the remaining rock in the planet? My first thought (quick) is that no volume measurement has been referenced, only length, so not enough info to possibly answer. Not a math major, just an artist . What do I know? There is a unique answer, and knowing that helps solve the problem in your head in 30 seconds. Or you can use calculus and spend an hour over it. Well, it looks like the remaining toroidal bit might fit into a one cubic vmile box. Admittedly, no intuitive problem solving based on any math, just a couple of quick sketches and the hint that it can quickly be solved in your head. As an imaginary central cube gets bigger, so does the ring-shaped remains. Just a guess that the number is a whole number and it doesn't "look" like enough stuff left to fit 2 boxes. ETA - I'm changing my answer. I'm going with "half + a little" again. Quote Share this post Link to post Share on other sites
sacex250 0 #50 June 16, 2012 Here's a demonstration by a Harvard student.It's all been said before, no sense repeating it here. Quote Share this post Link to post Share on other sites
