Geometry

Hello Guest,

Yes, easy to do in one dimension - a straight wall for instance, and a straight line along it.

A straight line in two dimensions is more difficult, because the curvature of the Earth needs to be allowed for.

But space is curved, so what we perceive as a straight line, may be otherwise.

The other thing to think about, is how much lead is in the pencil, or ink in the pen.

Kind Regards....

NO, it impossible to draw a straight line.A line as a mere geometric construct...
or
YES, simple, It is done on many sports field.

It depends entirely on your definition of 'staight' and 'line'.

Del

Thanks. As far as our high school geometry is concerned, drawing a straight line is possible. But as per real geometry drawing of an accurate/ perfect straight line on curved surface of the earth is not possible. Then a long line like 100mtrs will also be not possible. Other points like lead of the pencil and maintaining straightness as far as possible are the practical drawing difficulties. But the fact is that if we keep aside the approximation then drawing a straight is not possible. Similarly the total of all 3 angles of a triangle is not 180 degree on curved surface of the earth. Just think all our calculation of Triconometry goes wrong if we keep aside the approximation. But still we live on approximation and do all calculations, which also becomes practical. But all our practical calculation is not real (if we think in deep and go for finer accuracy). We actually live in approximation, imagination or in illution.

Moving on to spherical geometry is changing the goal posts somewhat. It's also altered what you mean by 'straight'. Airlines would be in trouble if they couldn't work with spherical geometry. Drawing a 'straight' line on a sphere should be easier since we can rotate the sphere against the pencil.

This may help with the 'lead in a pencil' trouble. With care, you may be able to manage 550 lines. Occasional sharpening may reduce this figure. Some kind of laser guidance may be needed to ensure 'straightness' of line. A long piece of wallpaper on the side of a skyscraper would be a good stating medium. This would negate curvature of the earth, and also prevent air temperature differentials from skewing the laser guidance system. The pencil should be mounted on a rail and driven by a motor - some clever circuitry could apply the correct drwaing time. For accuracy, effects of wind resistance on the assembly should be taken into account. Slower rates of drawing will give greater accuracy.

"The pencil should be mounted on a rail and driven by a motor -"

Of course the rail itself must be straight or....

Of course, getting the rail straight is easy. Just draw a straight line and set the rail along side, and eye it up. Hammer where necessary.

If it is possible to draw a straight line of any length, it is possible to draw one 100 m long.

Any drawn line has three dimensions -- 2 too many for a real, geometric line.

Yes.

Use a drawing program with scalability.

My display is set such that the red box around the question appears to be a very generous 10" x 2". By holding the Ctrl key and using the scroll button, this can be enlarged considerably. Unfortunately my monitor can't cope with 100m, but it's a start.

How about a Peaucellier-Lipkin linkage ?

Here is more.

But how do we draw a straight jacket?

Furthermore, how do we draw a Strait George?

But how do we draw a straight jacket?

With lots of buckles.

Furthermore, how do we draw a Strait George?

I thought you were talking about Boy George and I was going to tell you your on your own.

Brad

Boy George ain't got a straight bone in his body.

Let's go back to Kris' pencil on a rail scheme for a moment. Suppose on a windless day we suspend a plumb bob from a 100 M cliff. At the point where it touches the ground, we attach it firmly (the top end is likewise attached firmly). Now, we unroll a sufficiently long roll of toilet tissue beside the plumb line (maybe Scott's 1000 sheets per roll).

With tissue attached top and bottom, we attach Kris' pencil to a trolley which rides freely on the plumb line. Place the pencil tip against the tissue and let go of the trolley. Wallah!! We've drawn a straight line.

Of course we need to select a location where gravitational anomalies are minimal.

-John

Yes, but ... will depend on your cushy hand, the surface and your tolerance concerning roughness.

Yes, use a laser and then adjust for the curvature of gravity.

Of course it won't last because the Earth, Moon, Sun, Universe dynamic.

I guess this is dependant on your definition of strait.

Brad

As far as I remenber (I am a 66 old/young chem eng) Euclides stated that a straight line is an infinite line going through two defined points. The frasing might not be correct but that's the general idea. I think its postulate nr 1 in the 1st book.

So how do you propose the original poster draw it?

Any straight line that you actually draw, will actually be a very long and skinny rectangle.

If we put a dot here and a dot there, would not the line exist between automagically, perfectly straight and non-dimensional

Depends how big the dot is.

this invention relates to a practical method of writing long straight lines on long pieces of paper, avoiding influences such as the curvature of the earth etc that may attempt to exert detrimental effects on the straightness of said written line.

take chosen length of paper and wind in a roll onto a damped, dispensing, rigidly held feed roller and feed said paper onto a damped, collecting, rigidly held collector roller, said feed roller and said collector rollers having precise axial parallelity, said collector roller having a powered drive arranged to pull the paper from the feed roller and collect it on the fed roller, much like in the papermaking process which is well known in the art and need not be described any further here.

hold chosen writing instrument in laterally precise, gravitationally vertical contact with the outer diameter of the unrolling coil of paper while allowing / forcing said writing instrument to feed in towards the centre of the unwinding roll as the paper unwinds, while also preventing lateral displacement of said writing instrument and while having means to refill said writing instrument with fresh ink as required, said refilling attachment needing no explanation here since such refilling methods are well known in the art.

turn on said collector roller's drive motor and monitor writing process, refilling said writing instrument with fresh ink, either manually or automatically as required.

aforementioned process can continue as long as operator can find paper rolls long enough to write on, and as long as sufficient ink supplies can be provided to refresh writing instrument with.

of course, the writing process will need to be held in abeyance occasionally to allow for maintenance of previously described rig, such maintennce may entail the replacement of bearings and other wearing parts that are essential to maintain the axial parallelity of said rollers and the precise and good working order of other essential parts, such as the writing instrument etc.

By any chance are you a lawyer for said Geometry?

just practicing my patent writing.

s it is possible to draw a 100m striaght line . u can have a trace while traveling and u can take example as train track 100m is not at all a problem