Maths seems to be a lot of peoples’ least favorite school subject, yet maths can be beautiful.

Who knew geometry could be put on graph paper? Analytical geometry does that.

Algebra an early bugbear for some but it is an elegant way to structure a problem to arrive at a solution. An offshoot is matrix mathematics.

The real hate or fear I think is induced by calculus. Two types of calculus, the differential calculus and the integral calculus.

There is also Boolean arithmetic and Boolean calculus. You might remember sets and Venn diagrams.

The weirdest offshoot of maths is topology.

To a topologist a vinyl record/CD/DVD and a teacup are exactly the same. Anybody know why?

And then there is simple subtraction and some can't do something as elementary as that.

Another ad hom.

So, a vinyl record and a teacup, how can they possibly be considered the same thing?

Told you topology was weird.

You can probably find the answer on google, but try without that.

Topologists consider things in terms of sides and edges. That is what is known as a clue.

OK, a teacup and a record are identical to a topologist because they are two surfaces (top and bottom, inside and outside) and two edges, one in the spindle hole, one formed by the teacup handle and one edge on the outside.

Most should know this one: Can you have a strip of paper (or road or railway etc) that has only one surface and one edge?

I reckon something will be ringing a bell for most.

Any bells getting louder anywhere?

Let you think about that.

You have probably heard that “Angles on one side of a straight line always add to 180 degrees.”

This was the fifth axiom of Euclid.

Is it true always?

Get a strip of paper, preferable not too wide or too long just for convenience sake. Some glue, sticky tape ready to hand.

Hold both ends close together and give one end a half twist so what was the top side is now the bottom side. Fasten the two ends together.

You now have a bit of paper that has only one side. True! Sides are separated by edges but the strip has only one edge!

Don’t believe me? Put the strip down, put a pen to it and start drawing a line on the strip, keep moving it towards the pen, keep going—and eventually you will come to where you started the line. No edges crossed—the strip has only one side! You could test it has only one edge in a similar way. Magic! No—maths!

Can anyone name the name of the strip we made? Cudgel those brains!

Poor neglected Möbius strip  :)

If you glued two together, and assuming you could pass some paper through the 4th (or whatever) dimension, you would make a Klein bottle, a bottle with no inside or outside!

Something easier, get a pair of scissors and cut the strip in half lengthwise, like you drew the line on the one surface. See what results.

That leaves our poor neglected straight line.

Can you have a straight line with more than 180°?

Can you have a straight line with less than 180°?

Anyone?

Jovial Monk wrote on May 2^nd, 2018 at 7:56pm:

Get a strip of paper, preferable not too wide or too long just for convenience sake. Some glue, sticky tape ready to hand. Hold both ends close together and give one end a half twist so what was the top side is now the bottom side. Fasten the two ends together. You now have a bit of paper that has only one side. True! Sides are separated by edges but the strip has only one edge! Don’t believe me? Put the strip down, put a pen to it and start drawing a line on the strip, keep moving it towards the pen, keep going—and eventually you will come to where you started the line. No edges crossed—the strip has only one side! You could test it has only one edge in a similar way. Magic! No—maths! Can anyone name the name of the strip we made? Cudgel those brains!

I made my strip of paper....and then....found your 'instructions' incapable of understanding or applying.
:-?

If you have made your Mobius Strip, having given one side a half twist, draw a line along its length, keep doing that—you will arrive at your starting point without having crossed an edge—the strip has only one side!

Jovial Monk wrote on May 2^nd, 2018 at 9:14pm:

If you have made your Mobius Strip, having given one side a half twist, draw a line along its length, keep doing that—you will arrive at your starting point without having crossed an edge—the strip has only one side!

Far car!  Observe!

https://www.youtube.com/watch?v=Z30c5wvoS_s

Exactly what I said.

Hmmm I thought everyone would have come across the Mobius strip at school.  :o

Start drawing a line along the length of the strip, keep going, you will come back to your starting point!

I followed your instructions.  First....my strip of paper was two inches long, half an inch wide.  Nowhere did you tell me get some sticky tape and do what is shown in the video.

So....no I will have another go.  And in the mean time....

https://www.youtube.com/watch?v=udhb7EH-Rk4

;D

The axiom that a straight line contains 180° is just an axiom, something basic accepted as true.

You can have a geometry based on a line containing more than 180°! Ha, your teacher never told you that, eh?

wiki:

Quote:

The essential difference between the metric geometries is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line ℓ and a point A, which is not on ℓ, there is exactly one line through A that does not intersect ℓ. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting ℓ, while in elliptic geometry, any line through A intersects ℓ. Another way to describe the differences between these geometries is to consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line: In Euclidean geometry, the lines remain at a constant distance from each other (meaning that a line drawn perpendicular to one line at any point will intersect the other line and the length of the line segment joining the points of intersection remains constant) and are known as parallels. In hyperbolic geometry, they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels. In elliptic geometry, the lines "curve toward" each other and intersect.

A mathematician a long time ago tried to prove that Euclid was right, that the classic mathematics was right. So he assumed a line had less than 180° and developed the geometry based on that axiom. His geometry went very well and he worked out principles and constructs etc—until he got scared, scared he might upset the classic geometry of Euclid—and suffer for it! Remember the fate of Galileo!

Okay.....yes.  It did what you said.  Here is some more:

https://www.youtube.com/watch?v=wKV0GYvR2X8

Try cutting the mobius strip in two lengthways.

Jovial Monk wrote on May 2^nd, 2018 at 9:54pm:

Try cutting the mobius strip in two lengthways.

::)

Anybody remember who invented calculus?

Was actually two people who invented calculus at the same time and independently.

One was a founding member of the Royal Society. The other wasn’t.

Anyone. . . . . .?

The two people who independently invented calculus at pretty much the same time were Isaac Newton and Gottfried Wilhelm Leibniz.

Newton invented the dot system for showing differentials in an equation

y=the variable

y' = the first derivative (it is meant to be a dot not an apostrophe  :)

y''' = the third derivative, etc. With a few inkblotches things could get hard to interpret. So the Leibnitz notation won out:

dy
dt

Is the “differential of y with respect to t”

dy or ∆y is read as delta y and dy/dt (not a real representation of it but the best I can do without a mathematical font) are read as “delta y with repsect to delta t or the differential of distance per unit of time.

t is often used to stand for time.

Most of you would have done the exercise in junior HS of drawing a circle on some graph paper and counted squares to get the area of that circle. Around the edge you count a square if it has more of it within the circle and reject a square if it is all or mostly outside the circle. Add up your squares and you have the area of your circle.

Imagine you start with graph paper with centimetre size squares. You can imagine that you would get a rough estimate of the area of your circle. So, you move to finer graph paper, 5mm squares then to graph paper with 1mm squares and go on a real bender and make graph paper with nanometer sized squares.

This idea of finer and finer measurements is what lies at the heart of differential calculus: we divide our graph paper into infinitesmal squares and we have differential calculus.

I NEVER use differential calculus you say. Yes you do, especially if you drive: you brake to avoid hitting another car, you press harder on the brake pedal if the bit of differential calculus in front of you shows you you will hit the car!

Differential calculus is involved in the infinitesimal changes as you approach the limit (but never get there, like the limit in traffic is the rear bumper of the car ahead of you—you don’t want to reach that limit, $$$$.

Some limits: a change in slope of some function like a parabola (remember parabolas? When you chuck a wad of paper at your waste paper bin that wad travels in a parabola and a cannon ball or shell travels in a parabola from the muzzle through the air until it hits the ground.) The acceleration needed to just escape the gravity of Earth etc.

Imagine you are making a trip, just a short one, by foot. You walk at a certain pace that covers so much ground an hour, 5Km an hour say. so your ds/dt is your velocity, change in distance covered per unit of time.

Now let us decide the trip is too long so you take the bus. The bus starts at the busstop and gets up to speed and moves along at a steady speed (obviously, a theoretical bus!) and we can calculate how long it takes to cover a certain distance, ds/dt again.

Whoa! Hold your horses there! Unlike a person starting to walk from standing a vehicle needs to accelerate to a certain speed and that takes time!

Acceleration = dv/dt, change in velocity in a unit of time. But dv = dt/ds so acceleration is a = d2r/dt2 or the second derivative of distance per unit of time. Acceleration is measured as meters per second per second.

Our artillery shell, our rocket just escaping earth gravity and you not hitting the car in front are in the equation of motion that involve not just a first but a second derivative.

Let you digest that.

Jovial Monk wrote on May 8^th, 2018 at 10:28am:

The two people who independently invented calculus at pretty much the same time were Isaac Newton and Gottfried Wilhelm Leibniz. Newton invented the dot system for showing differentials in an equation y=the variable y' = the first derivative (it is meant to be a dot not an apostrophe  ;) y''' = the third derivative, etc. With a few inkblotches things could get hard to interpret. So the Leibnitz notation won out: dy dt Is the “differential of y with respect to t” dy or ∆y is read as delta y and dy/dt (not a real representation of it but the best I can do without a mathematical font) are read as “delta y with repsect to delta t or the differential of distance per unit of time. t is often used to stand for time. Most of you would have done the exercise in junior HS of drawing a circle on some graph paper and counted squares to get the area of that circle. Around the edge you count a square if it has more of it within the circle and reject a square if it is all or mostly outside the circle. Add up your squares and you have the area of your circle. Imagine you start with graph paper with centimetre size squares. You can imagine that you would get a rough estimate of the area of your circle. So, you move to finer graph paper, 5mm squares then to graph paper with 1mm squares and go on a real bender and make graph paper with nanometer sized squares. This idea of finer and finer measurements is what lies at the heart of differential calculus: we divide our graph paper into infinitesmal squares and we have differential calculus. I NEVER use differential calculus you say. Yes you do, especially if you drive: you brake to avoid hitting another car, you press harder on the brake pedal if the bit of differential calculus in front of you shows you you will hit the car! Differential calculus is involved in the infinitesimal changes as you approach the limit (but never get there, like the limit in traffic is the rear bumper of the car ahead of you—you don’t want to reach that limit, $$$$. Some limits: a change in slope of some function like a parabola (remember parabolas? When you chuck a wad of paper at your waste paper bin that wad travels in a parabola and a cannon ball or shell travels in a parabola from the muzzle through the air until it hits the ground.) The acceleration needed to just escape the gravity of Earth etc. Imagine you are making a trip, just a short one, by foot. You walk at a certain pace that covers so much ground an hour, 5Km an hour say. so your ds/dt is your velocity, change in distance covered per unit of time. Now let us decide the trip is too long so you take the bus. The bus starts at the busstop and gets up to speed and moves along at a steady speed (obviously, a theoretical bus!) and we can calculate how long it takes to cover a certain distance, ds/dt again. Whoa! Hold your horses there! Unlike a person starting to walk from standing a vehicle needs to accelerate to a certain speed and that takes time! Acceleration = dv/dt, change in velocity in a unit of time. But dv = dt/ds so acceleration is a = d2r/dt2 or the second derivative of distance per unit of time. Acceleration is measured as meters per second per second. Our artillery shell, our rocket just escaping earth gravity and you not hitting the car in front are in the equation of motion that involve not just a first but a second derivative. Let you digest that.

Looks like a great site you found Momk , can you post a link ?

“Momk , ” ???

High School education, Maths I & Maths II, University Maths I and Maths Stats and Demographics.

Jovial Monk wrote on May 2^nd, 2018 at 9:54pm:

Try cutting the mobius strip in two lengthways.

Try three and see what you get

How to work out how deep a well is when you have no instrument to measure distance? We all know this, don’t we? Drop a stone into the well and count the seconds until you hear a splash, then work out distance s using a simple formula.

How does this work?

We know dv/dt don’t we? Hmmm? Anybody

Why do we know the acceleration of the stone? Anyone?

Now, the stone is constantly accelerating (a stone is heavy enough that for reasonably short distances air resistance is not a factor) so how the hell do we know the distance the stone fell from the time it took to fall? The deeper the well the faster the stone is travelling when it reaches the bottom of the well.

Integral calculus comes to the rescue—we integrate or sum up the infinitessimal segments of the travels of our stone.

Let us start with a simple summation of discrete values (discrete means no infinitesimals differential calculus freaks talk about

∑ or sigma is the sign for summation of a set of values.

Usually written as Sum of values of x=n for values of n from 1 to 6 (when we get to integral calculus we often sum a variable to infinity.

So ∑x from n = 1 to 6 is simply the sum of 1+2+3+4+5+6 = (let you work it out, don’t use your calculator, LOL!)

x=n is a boring kind of function. What is we create a function where x=n!

x=n? You said that was boring! Grasshopper, you missed the “!” or factorial sign. n! = n x (n-1) x (n-2). . . x1 so that 5! = 5 x 4 x 3 x 2 x 1 = 120

So, for n=5 to n=2 ∑ƒ(x = n!) = ∑ 5! + 4! + 3! + 2!

That is a simple sum. The integral of a function is a bit more complex but it lets us work out areas or volumes or whatever of irregular shapes or volumes etc. How much fuel does a rocket need to escape earths gravity then set course for Mars at a set speed? Back to “delta v” but now we need to add up all the fuel needed to provide the various delta vs.

OK, see if anyone can give an answer.

We want to know how deep a well is but we have no way of measuring distance. We drop a stone into the well then count the seconds until we hear the splash, do a calculation an know how deep the well is. How does that work, what is the formula?

The rock will constantly accelerate until it hits the water in the bottom of the well. Why? Any idea of the actual acceleration?

Will leave the above for a bit.

I said the stone keeps accelerating (because. . . .?) but for long distances that is not true and lucky too!

Say you are caught in the rain. If the raindrops fell from the clouds and kept accelerating they would split your skull if they landed on your head!

Fortunately, air resistance slows the drops so they never fall faster than what is called “terminal velocity” big drops fall a bit faster than smaller drops or the terminal velocity of a bigger drop is higher.

What about hail? Hail is formed even higher in the atmosphere than rain.

Hail starts as rain in a big thunderstorm then convection in the thunderstorm sends the rain high up in the atmosphere where air pressure is less so the air expands and cools and freezes the water. When it has accumulated a certain mass the little hailstone will be heavy enough to fall through the updraft and fall but it can be sent up again when it reaches the zone of strong updraft in the storm.

Hailstones can stick together producing a “spiked appearance.”

Golfball-sized hail is not uncommon tho fortunately most hail is more like 5mm across in size. Very fortunate that air resistance limits the speed at which hail hits you!

As you can see (and read up wiki on hail formation) surface temperature does not cause more or less hail to form: hail is not a sign of an ice age tho the mentally deficient think that it is.

Jovial Monk wrote on May 9^th, 2018 at 10:47pm:

How to work out how deep a well is when you have no instrument to measure distance? We all know this, don’t we? Drop a stone into the well and count the seconds until you hear a splash, then work out distance s using a simple formula. How does this work? We know dv/dt don’t we? Hmmm? Anybody Why do we know the acceleration of the stone? Anyone? Now, the stone is constantly accelerating (a stone is heavy enough that for reasonably short distances air resistance is not a factor) so how the hell do we know the distance the stone fell from the time it took to fall? The deeper the well the faster the stone is travelling when it reaches the bottom of the well. Integral calculus comes to the rescue—we integrate or sum up the infinitessimal segments of the travels of our stone. Let us start with a simple summation of discrete values (discrete means no infinitesimals differential calculus freaks talk about ∑ or sigma is the sign for summation of a set of values. Usually written as Sum of values of x=n for values of n from 1 to 6 (when we get to integral calculus we often sum a variable to infinity. So ∑x from n = 1 to 6 is simply the sum of 1+2+3+4+5+6 = (let you work it out, don’t use your calculator, LOL!) x=n is a boring kind of function. What is we create a function where x=n! x=n? You said that was boring! Grasshopper, you missed the “!” or factorial sign. n! = n x (n-1) x (n-2). . . x1 so that 5! = 5 x 4 x 3 x 2 x 1 = 120 So, for n=5 to n=2 ∑ƒ(x = n!) = ∑ 5! + 4! + 3! + 2! That is a simple sum. The integral of a function is a bit more complex but it lets us work out areas or volumes or whatever of irregular shapes or volumes etc. How much fuel does a rocket need to escape earths gravity then set course for Mars at a set speed? Back to “delta v” but now we need to add up all the fuel needed to provide the various delta vs. OK, see if anyone can give an answer. We want to know how deep a well is but we have no way of measuring distance. We drop a stone into the well then count the seconds until we hear the splash, do a calculation an know how deep the well is. How does that work, what is the formula? The rock will constantly accelerate until it hits the water in the bottom of the well. Why? Any idea of the actual acceleration?

Gravity is 9.81 m/2 you will also need to take into account the speed of sound to get a truely accurate measure of its depth

Very gourd!

Can you give us the formula to convert time of fall to distance fallen?

Jovial Monk wrote on May 10^th, 2018 at 3:10pm:

Very gourd! Can you give us the formula to convert time of fall to distance fallen?

Not off the top of my gourd, but it wouldnt be to hard to knock up,

OK, waiting. . .

Jovial Monk wrote on May 10^th, 2018 at 5:28pm:

OK, waiting. . .

Been a long day , a couple of bourbon and cokes ,a little to chilled for it lol

BigP wrote on May 10^th, 2018 at 5:33pm:

Jovial Monk wrote on May 10th, 2018 at 5:28pm: OK, waiting. . . Been a long day , a couple of bourbon and cokes ,a little to chilled for it lol

Are you in NZ?

BigP wrote on May 10^th, 2018 at 5:33pm:

Jovial Monk wrote on May 10th, 2018 at 5:28pm: OK, waiting. . . Been a long day , a couple of bourbon and cokes ,a little to chilled for it lol

Yeah, I had a really nice long lunch at the Skillogalee winery near Clare today, I don’t feel full of energy either—just woke up from a nice nap!

Nice glass of their rosé and one of their shiraz to go with the Angus ribeye. Desert was delicious: a chocolate mousse with a raspberry sorbet, yum!

Aussie wrote on May 10^th, 2018 at 5:34pm:

BigP wrote on May 10th, 2018 at 5:33pm: Jovial Monk wrote on May 10th, 2018 at 5:28pm: OK, waiting. . . Been a long day , a couple of bourbon and cokes ,a little to chilled for it lol Are you in NZ?

That would be an affirmative. Auckland

Jovial Monk wrote on May 10^th, 2018 at 5:42pm:

BigP wrote on May 10th, 2018 at 5:33pm: Jovial Monk wrote on May 10th, 2018 at 5:28pm: OK, waiting. . . Been a long day , a couple of bourbon and cokes ,a little to chilled for it lol Yeah, I had a really nice long lunch at the Skillogalee winery near Clare today, I don’t feel full of energy either—just woke up from a nice nap! Nice glass of their rosé and one of their shiraz to go with the Angus ribeye. Desert was delicious: a chocolate mousse with a raspberry sorbet, yum!

A nap. sure it wasnt a diabetic coma lol

I was thinking of retiring to NZ but decided, no. Hence the block of land in Tasmania. Like NZ but without the accent  :)

I also thought whether to go back to Holland but very quickly decided only for a visit!

BigP wrote on May 10^th, 2018 at 5:44pm:

Aussie wrote on May 10th, 2018 at 5:34pm: BigP wrote on May 10th, 2018 at 5:33pm: Jovial Monk wrote on May 10th, 2018 at 5:28pm: OK, waiting. . . Been a long day , a couple of bourbon and cokes ,a little to chilled for it lol Are you in NZ? That would be an affirmative. Auckland

Three hours out of whack.  Bed time for you.

Jovial Monk wrote on May 10^th, 2018 at 5:47pm:

I was thinking of retiring to NZ but decided, no. Hence the block of land in Tasmania. Like NZ but without the accent  :) I also thought whether to go back to Holland but very quickly decided only for a visit!

Yes....and no Kiwis.

Kiwis are alright. Seems they know how to play rugby where we don’t  ;D

Been having fun doing this. Sort of revising my rusty maths. I did love studying maths in senior HS and at Uni.

When you do tensor calculations you end up with situations where

    a + b ≠ b + a

How wacky is that? Bit beyond BODMAS  ;D

Love to find a decent book or two and a youtube channel about maths: not a HS text more sort of “appreciaton of maths.”

In the stats part we used statistical calculators. Plug in a value, pull the handle and the machine would calculate ∑ and the square and the sum of the squares—the standard deviation being the sum of the squares minus the square of the sum kind of thing.

Nowadays—all done in spreadsheets I suppose and there are statistical packages like SPSS—Statistical Package for the Social Sciences. Used part of that in my marketing studies—running on a PDP11 minicomputer. Personal computers came in a little later, I bought my TRS80 in 1979.

Aussie wrote on May 10^th, 2018 at 5:51pm:

Jovial Monk wrote on May 10th, 2018 at 5:47pm: I was thinking of retiring to NZ but decided, no. Hence the block of land in Tasmania. Like NZ but without the accent  :) I also thought whether to go back to Holland but very quickly decided only for a visit! Yes....and no Kiwis.

We are likeTasmanians but with better english skill

BigP wrote on May 11^th, 2018 at 3:29pm:

Aussie wrote on May 10th, 2018 at 5:51pm: Jovial Monk wrote on May 10th, 2018 at 5:47pm: I was thinking of retiring to NZ but decided, no. Hence the block of land in Tasmania. Like NZ but without the accent  :) I also thought whether to go back to Holland but very quickly decided only for a visit! Yes....and no Kiwis. We are likeTasmanians but with better english skill

Well, if you are par for the course on that....nah.

Aussie wrote on May 11^th, 2018 at 3:36pm:

BigP wrote on May 11th, 2018 at 3:29pm: Aussie wrote on May 10th, 2018 at 5:51pm: Jovial Monk wrote on May 10th, 2018 at 5:47pm: I was thinking of retiring to NZ but decided, no. Hence the block of land in Tasmania. Like NZ but without the accent  :) I also thought whether to go back to Holland but very quickly decided only for a visit! Yes....and no Kiwis. We are likeTasmanians but with better english skill Well, if you are par for the course on that....nah.

Thats only because you are scoring the Tassies to high. showing a little bias im thinkin

Quote:

Thats only because you are scoring the Tassies to high. showing a little bias im thinkin

No need to thank me.

Aussie wrote on May 11^th, 2018 at 3:45pm:

Quote: Thats only because you are scoring the Tassies to high. showing a little bias im thinkin No need to thank me.

I was of a mind to give you a good tikin off  :-*

A 10 ton spaceship can burn enough fuel at a constant rate so that at the start of the voyage acceleration is just enough to reach the planet Mars where it will be.

The orbit of Mars is reached too early and Mars is still far from the point the spaceship should reach it. What went wrong?

We know that Force = mass times acceleration, or:

F = m x a

You have enough data to work out the answer.

Nobody?

Let me rearrange the equation

a = F/m

The answer is in that equation!

Don't expect anything from me on that stuff!  You are talking Martian.

Where is Lee?  (He's the bloke who uses a big word...sounds very mathematical too......algorithm.)

:o

Hiding.

His incandescent intellect could not work out that water under a thin crust of ice could not freeze anything that fell into it, let alone flash freeze anything. If he can’t find anything on a denier site he is lost, basically.

Jovial Monk wrote on May 14^th, 2018 at 4:29pm:

Nobody? Let me rearrange the equation a = F/m The answer is in that equation!

m, mass of the spaceship.

At the start, it has full fuel tanks, m is at a max. As the rocket burns fuel the mass of the spaceship (including fuel tanks) decreases and, given the constant force F from burning the fuel, acceleration increases.

Exactly WHERE the spaceship would end up can be solved using integral calculus (the sum of the infinitesimal fractions of time and the infinitesimal decrease of mass of the spaceship.

Theoretically this holds for cars, ships etc etc but they face a punishing regime of friction meaning the effect of decreasing mass is lost. A spaceship faces stuff all friction (unless it hits a meteorite etc  ;D )

(This is from a humorous SciFi story set in the asteroid belt. Some asteroids are very close together.)

The head brewer on an asteroid becomes aware his asteroid is being invaded. How can he escape to reach a nearby asteroid to raise the alarm?

Every action brings forth an equal and opposite reaction.

So. . . .?

Jovial Monk wrote on May 14^th, 2018 at 5:27pm:

(This is from a humorous SciFi story set in the asteroid belt. Some asteroids are very close together.) The head brewer on an asteroid becomes aware his asteroid is being invaded. How can he escape to reach a nearby asteroid to raise the alarm? Every action brings forth an equal and opposite reaction. So. . . .?

Fuqed if I know.  I guess the invasion/invaders brings some energy with their action, and he can somehow take advantage of it?  They nudge his asteroid and that allows it (through movement) to allow him to make the jump?

Dunno.

:-?

Lashes a few kegs to a framework, connects them together—pssssttttttttt the beer rocket takes off. Just needs a gentle delta v as asteroids have negligible gravity.

Wouldn’t work with British real ale (warm and flat  ;D ;D ;D ;D ;D)

Remember—chuck something, rocks would do tho delta v is miniscule—and action engenders reaction and your spaceship moves in the direction opposite to where you sent surplus mass.

In the asteroids gravity can be pretty much disregarded, you just want enough delta v to reach where you want to go.

OK, keeping in line with all this:

In a few Loony Toons one character gets his sail boat to move by directing a fan onto his sails.

Why won’t that work in real life? (ignore resistance of air to the stream from the fan etc and assume the fan is powered by an infinitely huge battery, think action and reaction)

Jovial Monk wrote on May 14^th, 2018 at 5:44pm:

OK, keeping in line with all this: In a few Loony Toons one character gets his sail boat to move by directing a fan onto his sails. Why won’t that work in real life? (ignore resistance of air to the stream from the fan etc and assume the fan is powered by an infinitely huge battery, think action and reaction)

Where is the fan positioned?  On the boat?

Yeah yeah, on the boat.

If it's on the boat....it would push the boat backwards unless there was a stronger (natural) wind.

Do I get a brown paper bag of Uncanny's boiled lollies?

Well, nah, not really.

The fan sends air forwards—that sends the boat backwards.

The air hits the sails—that sends the boat forwards. Result—boat does not move a millimetre.

Boats can be powered by a fan—we have seen swamp buggies with a big fan on the rear. But a fan can’t make the boat move by sending a stream of air on the sails.

Look at it this way: if your heels were right on the edge of an abyss you would not throw a big rock away from you—you would know that would send you over the edge. Well, not the throwing of the stone, the equal and opposite reaction to pitching the boulder.

Quote:

The fan sends air forwards—that sends the boat backwards.

Isn't that what I said?

Yes it is ya Scrooge!  Gimme my brown paper bag of Uncanny's boiled lollies!

Not really maths but what the hell:

https://pbs.twimg.com/media/DdJ6t2OW0AAm1CB.jpg