## Introduction: Six-pointed Paper Snowflake Cutting Instruction

The technique of making a paper snowflake of regular hexagonal shape by cutting it out of a sheet of paper with scissors. Detailed step-by-step instruction in the form of video, comics, text descriptions. Theory: how to cut a regular hexagon without a pencil, ruler or compasses

## Step 1: Theory. How to Make a Regular Hexagon

This method is based on the following geometric pattern (see the picture 1):

A regular hexagon is drawn on a square piece of paper. We see that the hexagon is symmetrical about the axes of the tetragonal leaf, so you can fold the leaf in four and cut out all the layers only in one quarter. Further, we see that, in theory, the vertex of the hexagon, A, lies on the middle (green) vertical line of the quarter. Therefore, in order to find this point A, you first need to bend the quarter in half and the fold line will mark this green line for us. Then, using the fact that the segment CB is equal to the segment CA, take the corner B of the leaf and pull it up along the green line until the edge of the CB leaf stretches and becomes straight, and a clear bend forms in the corner C (see the picture 2). Then point B on the inflection (green) line marks us point.

## Step 2: Instruction in Pictures

A detailed description of what is happening in the pictures.

①② Fold the square leaf in four.

③ Fold back half of the quarter to obtain the midline indicated by the bend.

④ Bend the corner of the quadrilateral to the marked midline.

⑤ It is necessary that the corner of the quadrilateral "fall" exactly on the center line, and in the corner, which is indicated by the exclamation mark, an inflection forms exactly from the corner of the square.

⑥ We have three key points: A is the required vertex of the hexagon, b is the 1st corner of the quadrilateral and also the vertex of the hexagon, c is a point located at the same distance from the left side of the square as point A.

⑦ Cut all 4 layers of the square from point b to A and from A to c. This is best to do by eye. If the cut turns out to be uneven, it doesn't matter, all the sides of the hexagon will still be patterned out further.

⑧ Expand the piece of paper - 6-sided regular polygon. Fold it in half.

⑨ ⑩ ⑪ ⑫ ⑬ ⑭ Fold it 6 times into an accordion-triangle.

⑮ Draw a triangle with a grid of lines parallel to the top edge, right edge, and at 60 degrees. A natural real snowflake made of ice has not only 6 rays, but all the crystals inside are hexagonal.

⑯ Draw a pattern, observing the "law of 6-sidedness" - the angles of the broken lines are 60 and 120 degrees. We cut along these contours.

⑰ ⑱ The result.

## Step 3: Video: How to Cut a Regular Snowflake of Paper

4 examples:

Pay attention: the last snowflakes in the video are made without a pencil, ruler or compasses - bending of paper and scissors only. To make so, first, cut along a line parallel to the side of the square and passing through point A. It is not necessary to mark this point A with a pencil, you can leave the corner B/b of the leaf there. Then cut off from point b to point A, which is now just the point of intersection of the middle (green) line with the side of the rectangle.