6

If I am trying to draw a rectangle or square on a piece of paper I can use existing corners of the paper as a start point. However I lose accuracy when completing the square or shape on the inside of the paper. In some cases I plan on cutting this and using it a template.

I measure corner to corner to verify accuracy and I usually have to settle for good enough.

If I had a square (ruler) I don't think I would be having an issue or at least not be adjusting my lines as often.

Using just a plain ruler and pencil is it possible to draw a perfect or near perfect square or rectangle? i.e. set of 4 right angles.

  • 1
    Break the ruler in half. Glue the halves together at a right angle. Now you get perfect right angles every time. :) – Web Head Aug 15 '18 at 20:22
  • @WebHead I said using only a ruler......:) – Matt Aug 16 '18 at 16:13
  • I knew you'd say that, so I decided you could use the ruler's sharper edges to saw out a cross lap joint, stick the two halves together, and voila! – Web Head Aug 16 '18 at 17:59
  • 1
    Well aren't you crafty – Matt Aug 16 '18 at 17:59
  • It is impossible to draw anything with a just ruler. Pencils, pens, chalk and even paint brushes are far better at drawing than rulers. – Henry Taylor May 16 at 14:03
14

You can use the 3-4-5 method of creating right angles.

Begin with a construction line and mark a zero point and a 3 point. Make a mark. Notice that I'm not using units of measure. You can use millimeters (preferred) or inches or anything in between.

Draw from the zero point at a right angle as closely as possible. Measure from the zero point to a 4 point. Make a mark.

Measure from one of the marks to the other and it should be a 5 point. If so, you have your right angle.

If not, you will have to erase or otherwise ignore the second line and create yet another.

I prefer using metric measurements for this type of project. You can adjust the numbers to fit your workspace. Let's say that you have a small piece of paper on which you wish to create your square.

The first line could be 90 mm long (3 * 30), while the second line would be 120 mm (4 * 30) and the points should be 150 mm apart (5 * 30).

Instead of drawing the second line as described above, consider to have a piece of paper with the length necessary for the conditions (120 mm) and position it with the zero point on the first line. Move the paper in an arc until it meets with your 150 mm point on the ruler. You can then mark the base paper with your points for a perfect square without having to erase misplaced lines.

As noted in the image below, greater accuracy is gained with larger distances. The quality of the measuring instrument also plays a factor, but only a minor part.

3-4-5 right angle

  • 1
    I wish I could flag this answer as being dangerously awesome. – Nothingismagick Aug 13 '18 at 17:41
  • 1
    Does Pythagoras know about this? – Web Head Aug 16 '18 at 17:59
  • Shout out to the ancient Egyptians, who also used the 3-4-5 method to create right angles - before Pythagoras existed: storyofmathematics.com/egyptian.html – Flora Su May 10 at 16:50
  • You suggested using multiples of 3, 4 and 5, but you can also use fractions too. 1.5, 2 and 2.5 (halves of each) would work. Fractions of multiples would also work. Half of the 9, 12, 15 (4.5, 6 and 7.5) for example. – Chris Rogers May 22 at 4:23
4
  1. Draw top and bottom of the ruler to create parallel lines.
  2. Rotate the ruler and repeat using the original lines to create a parallelogram.
  3. Draw the diagonals of the the parallelogram, thus creating a right angle at the centre.
  4. Continue drawing parallel lines with same width using the ruler and adding the diagonals.
  5. A square will present itself. enter image description here.
  • Loving it. Nice answer and welcome to Arts & Crafts.SE – Matt May 16 at 11:21
  • This is the best answer: it's simple and efficient. – Joachim May 16 at 16:06
  • I've upvoted this answer for its simplicity. – fred_dot_u May 22 at 12:58
2

This is not possible using only a ruler. The only way I know of to do this in the physical universe as absolutely perfectly as possible is to use a compass and a straightedge. This method requires no measuring, but only accuracy.

enter image description here

  1. First draw a circle, making sure to leave a mark at the center.
  2. Pick any point on the circle as the position for the center of a circle with the exact same radius.
  3. Draw a line through these two radii and use the intersection of line and circle to place the center for the third circle and draw one there.
  4. From the center outward, draw lines through the intersections of conjoining circles. Where these lines meet, draw a line down the center to construct your perpendicular and solve for the bisection of the circle.
  5. Connect the dots.

Image is my own work. CC-BY

  • Of course, if you have a ruler with a hole in it and a second object to rotate it about, you could use it as a makeshift pair of compasses... – walrus Aug 15 '18 at 16:34
  • Well, that would still be a straightedge and a compass- albeit in one object. ;) – Nothingismagick Aug 16 '18 at 0:17
  • For what it is worth, this technique can also be applied to spheres, albeit with a string instead of a ruler. – Nothingismagick Aug 18 '18 at 9:50
  • "This is not possible using only a ruler" - but other answers prove it is. – Joachim May 16 at 16:06
  • @Joachim - my understanding of a right angle was a geometrically perfect one, and the other approaches are approximations, albeit close - like how 22/7 is almost the circle constant. Your reading of this would imply that it’s also ok to just use the corner of a ruler because that’s also close enough to 90 degrees. They also suggest that it’s ok to use a piece of paper and fold it. – Nothingismagick May 21 at 20:03
0

If you're planning on cutting anyway fold the paper. For squares you can measure along your straight edges and then fold up a triangle using your 2 marks for your corners. You can then trace the edge of the paper to get the other sides of the square.

Rectangles you can fold each side.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.