When liquid spins, it makes a parabola surface. and that's a good stuff for astronomors

**Liquid-mirror telescope set to give stargazing a new spin**

**http://www.europa.com/~telscope/LMT.txt**

it's really amazing to see these inventions are made little by little rather than spontanously.

]]>Let's take a break and appreciate some history.

The first modern suspension bridge ever built is Brooklyn Bridge, which connects Manhatten and Brooklyn, New York. The idea came from a German immgrant engineer, John Augustus Roebling . Avant as he was, he prepared 2 years from 1867 for every detail before start, and worked for 14 more years before he died of an infection.

His son Washington, also an engineer and bridge builder, took over his father's dream. He and his wife co-si[ervised the construction and completed the bridge.

The Brooklyne Bridge

Total Span: (Measures the distance between the two anchorages.) 3,455 feet

Main Span: (Measures the distance between the two towers.) 1,595 feet

Height of the Towers: 276 feet

Engineer(s): John Roebling, Washington A. Roebling

Cost: $15 million

Washington and his wife

Yes, you could say so. but to be exact, near. because matter is made of sufficient smalls instead of continuous infinite smalls.

My point is, most of caculus's success is built on descrete approximation.

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But if we had a bridge that had only one hanger that was planar across the entire main cable, then it would be parabolic.

Of course, then the massive weight of this planar hanger is going to have to be considered.

]]>But if we only plotted the points were hanger meets main cable, then we have a parabola.

But if we had a bridge that had only one hanger that was planar across the entire main cable, then it would be parabolic.

]]>NOTICE the KNOTS (corrected), they are streched downward.

Franklin's guess is right, too. Even the knits doesn't form a parabola but a parabola-catenary mix.

For Post 12, you cannot get a parabola knits trajectory.

the tangent (slope) grows by 0, 2, 4, 6

height grows by 0, 2, 6, 10 =n(n+1)

length l= (n-1/2)Δx set Δx=1 n=l+1/2

n(n+1)= (l+1/2)(l+3/2) the function of right knits isn't symmetric about the axis in the graph, thus left knits have another function (l-1/2)(l-3/2)

Two parabolas

A lot of films have such a horrible scene:

heros dashing on a broken rope bridge, and luckily reaching the end.

The rope , similar to the cable of a suspension bridge, should break near one end, rather than in the mid point-- you may verify this.

]]>**n,m,g,W,+**

if we name the mid verticle cable the 0th verticle, we can also name all five verticle cables -2nd verticle, -1st verticle, 0th verticle, 1st verticle and 2nd verticle. and then we can define on each Δx is distributed with same mass m. g represents acceleration due to earth gravity.

1/2mg=def=W hence mg=2W

at the upper end of nth verticle(the tri-knit), forces are always 3, one downward(gravitional force), one leftward, and one rightward. define horizontally rightward and verticly upward +,and use cartesian expression of vectors. Using Newton's 1st and 2nd Law,we will easily get the table below.

nth 0 1 2 3 (not displayed in graph)

leftwardforce (-h*,W) (-h,-W)# (-h,-3W) (-h,-5W) *h is unkown

rightwardforce(h,W)# (h,3W) (h,5W) (h,7W)

LF tangent -- W/h 3W/h 5W/h

height-increament-- (W/h)Δx 3(W/h)Δx 5(W/h)Δx

height 0(set) (W/h)Δx 4(W/h)Δx 9(W/h)Δx

distance 0(set) Δx 2Δx 3Δx

# (h,W) and (-h,-W) are anti each other (Newton's 2nd Law)

at nth knit, LF+RF=2W, always(from 1st Law)

hence height= C distance², ignoring measure

but if the main cable behave more like a soft rope rather than a solid dome, it will bend more at the knits, thus not perfect parabola.

]]>Answer: Click on the tiny picture and it gets bigger. This confused me once too.

I think George said near-parabola because the weight of the cables throws it off slightly, but probably only millimeters.

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