The context is about drawing curves on a paper.

I cannot fathom why you would ever need to give this direction ha but I will give it a shot. I don't think your description is descriptive enough. To get this result I would say something like: "Draw a shallow arch that is one inch wide from right to left. Then, from the left end point of that arch drop a curved line upwards at a 60 degree angle." That isn't very good but this is a very weird shape that no one would normally be exposed to that you're asking to be drawn so you need to be very specific.

“Draw a curve to the left” could mean so many things. Describing shapes such as this in an unambiguous way in English is just difficult, even for native speakers. The more detailed your description, the better.

The first 2 are both fine. The third doesn’t seem natural at all.

None of the examples give enough detail on how to draw this shape. If I, personally, had to write instructions for this, I might say something like: "Imagine that the point where your pen touches the paper is the 12 o'clock position on a clock face. Draw a semicircle anticlockwise from the 12 o'clock position to the 5 o'clock position. Do not lift your pen. Now imagine a new clock face. Your pen is currently resting on the 9 o'clock position. Draw a semicircle clockwise from 9 to 3." It's a little bit of a long and convoluted way to explain it but it's the clearest way that I can think of to explain the direction of the curves, the concave/convex nature of them, and the start and end points.

Option 1 or something like “draw a line curving to the left then, starting at the base of the first line, draw a line arcing up at 60 degrees

Plot two points on the paper in said positions, then create a curve from one point to another. Plot another point at said location and draw a curve from the last point to the recent one.

If I had to describe this to somebody, I'd say: "Draw a tall letter C. At the bottom of the C, connect another one facing down like a lowercase n."

I attempted to create instructions, though it only really applies if you intend for 1) the curves to be half-ovals and 2) the curves to be congruent. The sentences you wrote are grammatically correct as far as I can tell (although "in the left direction" is an unnatural way of saying "to the left") but horribly ambiguous depending on your intentions. >Draw the top half an oval such that its major axis (the line crossing the two points of the oval farthest from each other) is horizontal. Draw a second copy of the shape rotated 120 degrees counter-clockwise about the leftmost point of the initial half-oval.

1 is OK, sort-of, but it doesn't say 60° from where - I'd probably have gone clockwise. 2 & 3 are weird. Not normal English. To write a native sentence, I'd need to understand what you want. But I'll try, based on the image.... I assume we know where they start? ... "Draw an upwards curve to the left, like a big, flat backwards letter "n", about 1/3 of the page width. Then, from the bottom left of that, draw another left-hand curve up, like a letter C, at about -20° - leaning to the left"

I’m a native speaker and I don’t know how I would describe that

Not a native, but I have an engineering background. This is how I would say it without using too much jargon: Draw 2 connected curves with the following instructions: 1) start right to left, drawing a curve horizontally, with the ends of the curve curving downward. 2) then draw a second connected curve starting from the left end of the first curve with an upward chord inclined at about 120-degree in the x-axis, making the ends of this curve point to the right. - This is very difficult to describe without using more geometry terminology

"Draw a vertical arch that points to the left-hand side, then from its bottom endpoint, draw a horizontal arch that points upward at 60 degrees."

Draw a line up that curves to the left Draw a second line at the base of the first going right that curves upwards

I would say “Draw a curve from down-left to down-right, ending directly below where it begins” or “draw the leftmost sixth of a circle” for the first arc, then “a curve from up-right to down-right” or “the top sixth of a circle” for the other part. There really is no commonly understood method or shorthand for what you’re asking about, but I think this way of describing it should be generally understood by everyone

You could use the words convex and concave maybe, but as others have pointed out this shape above would be very difficult to describe with words alone

There is a very famous children's party game where you do this. You get everyone to sit separated from each other with a piece of paper each, so they can't see each other's papers. You then give a series of instructions as to what to draw, and you draw what you're instructing to draw yourself. You do this for a number of steps (five, seven, any number really, just more than one, the more the better). Then you look at what everyone has drawn. Spoiler alert: the drawings will be vastly different from each other. The kids all see how different people interpreted the instructions and laugh at how silly each other must be. It's a good way for young children to learn about how different people interpret things in the world differently. In a word: there is no generalised clear instructional language for drawing in any language as far as I'm aware, certainly not in English.

Lots of ways to describe this. The issue is that this is a very specific request that English doesn't have concise terms for, at least not in common use. In cases like this, you could describe things with very technical terms. These shapes are parabolic arcs and you might even give a formula to describe their shape and arrangement. Maybe there are extremely uncommon terms to describe this specific arrangement of arches – would your reader understand those terms? There is a good chance that using uncommon or super technical language just ends up being counter-productive. I write technical manuals for a living and this is a case where I would just include a labeled diagram. If I had to describe this verbally, I would describe the locations of 3+ points along each curve and then tell the reader to connect the dots to create two shallow arches. I might even describe the orientation of each arch. The more important a precise understanding is, the more points you could describe. Sometimes, instructions like this are important enough to an organization that they create their own language to describe it. Militaries use formations and topologists have words for many more shapes and patterns than the average person. Again, your audience is key. Is it worth learning jargon/esoteric terms to describe this concisely or are you trying to make it as simple as possible? Can you use a diagram? The first questions professionals ask in cases like these are directed at simplifying as much as possible. I doubt the average reader of my manuals could follow even the most simplified textual instructions for this precisely. This is a fun exercise, though. Here's my take, assuming precision matters enough to use tools: Draw a dot on the center of your page. (Some distance, x) to the right horizontally, draw another dot. Find the middle point between these dots. (Some distance, y) perpendicularly up from that middle point, draw another dot. Create a continuous, smooth arch that connects all three dots, ideally covering them. Return to the first dot you drew. Measure 120° (oriented up) from an imagined straight line connecting the first and second dots. (120° because the visual example you gave shows an obtuse angle relative to the markers the reader already has.) (Some distance, x) along the 120° line, make another mark. Find the middle point between that mark and the first. Imagine a straight line between them and find the middle point of that line. (Some distance, y) Perpendicularly (and towards the right) from this middle point, draw another dot. Create an continuous, smooth arch that connects all three dots. This solution is long and dense, but a smart middle schooler (so hopefully at least half of adults) could follow along with tools. Again, compare that to a diagram with labeled steps or even a picture. You get just as much (if not more) precision, less error, and it is a simpler endeavor for the writer and reader alike. Language is flexible and there's a lot you can do with it, but *should* you try to do all of those things? Thanks for the fun question! And thanks to everyone else who replied. This is my first post here–seems like a fun community!

I would describe the angle using a clock face. If the lines were straight, you might say something like, "Starting from a central point, draw a 1 inch line to 3 o'clock and a 1 inch line to 11 o'clock." The curves would need to be described in more detail but I would still use the clock face for the angles. If you use degrees, you have to hope the other person has a pretty good idea what they look like and uses the same starting point as you.

"Draw a vertical line downward that curves to the left, then, starting at the end point of the previous line, draw a horizontal line rightward that curves up" You can use letters to describe shapes pretty effectively "Draw an uppercase L where the vertical bar curves outward to the left and the horizontal bar curves upward" the vertical bar has rightward facing concavity and leftward facing convexity. The bottom bar has downward facing concavity and upward facing convexity. Such terms might be helpful in your quest for describing this I wouldnt say "draw a curve". I would say "draw a curved line". But maybe thats just my predisposition towards math

Sorry, what do you mean?

I would say arch instead of curve for the first one so as to orientate the curve

I don't think any of the descriptions are accurate enough to let me deduce the intended figure. I'd require something like:  "Draw an arc of a circle starting at the 11:00 position and continuing all the way down to the 7:00 position. Then, without lifting your pen, begin a new arc of approximately the same radius, starting at the 10:00 position and ending at the 2:00 position."

The best I can do: "Draw a curve vertically with the curve going left and the two ends of the curve approximately aligned with each other. From where you left off, draw a horizontal curve with the curve going upward with the two ends of the curve approximately aligned with each other." Edit: You should also probably put in something about the distance apart the end of the lines should be from each other. Your instructions would end up with many variations of shapes.