Equilateral Triangle
Equilateral Triangle
Welcome page
Back to the list
|
|
Equilateral Triangle |
|
Folding sheets Equilateral Triangle Welcome page Back to the list |
Aveuglami project - folding sheet
Equilateral Triangle
| Author | Diverse |
| Category | orimaths |
| Difficulty | ** |
| Format | square |
| Base | - |
| Text | A triangle having its three sides of the same length (or its three angles of the same size) is said to be equilateral. Two methods of constructing an equilateral triangle are described below.
Method 1 - A4 format 1. Take a rectangular sheet (e.g. A4) held in a vertical position. 2. Bring, using a valley fold from left to right, the right edge to the left edge. Unfold. 3. Bring the bottom right corner to the middle crease you just created. The fold starts from the lower left corner This fold is quite difficult to make. You must start by bringing the lower right corner to the middle fold, without marking the fold. We then prepare the start of the fold in the lower left corner, by pinching it very lightly. You must then adjust the position of the corner on the central fold until you obtain a very clear straight line segment. We obtain a quadrilateral (rectangular trapezoid) which carries a triangular flap linked by an oblique hinge fold. 4. Bring, through an oblique valley fold resting on the upper right edge of the triangular flap (smaller side), the upper right corner on the hinge fold. The right side of the rectangular trapezoid aligns with the lower hinge fold of the fold in step 3. We obtain an outline of a triangle whose left side is hidden at the top by part of the flap that we have just folded. 5. Fold back the part of the upper flap which protrudes, resting on the left side of the triangle. The triangular shape appears completely. 6. Bring the small triangular flap that you have just folded under the upper flap. 7. Flip the fold from right to left. We obtain an equilateral triangle whose surface is entirely smooth. Method 2 - Create a length template 1. Take a rectangular sheet of A4 format, hold it in a horizontal position. 2. Fold the sheet in half with a valley fold from left to right and top to bottom, on the diagonal from the top left apex to the bottom right apex. 3. Rotate the fold so that the hinge edge is located at the bottom of the form, horizontally. We obtain a shape composed of two triangular flaps which partially overlap. At the top of the figure, we identify two points, which correspond to the upper vertices of the two triangles. 4. Make a valley fold from left to right, perpendicular to the hinge fold and passing through the top of the upper left point. 5. Make a valley fold from right to left, perpendicular to the hinge fold and passing through the top of the upper right point. The two points that have just been folded each form a sort of pocket. 6. Slide the old left tip inside the pocket formed by the old right tip. We obtain a sort of dunce cap whose base forms the desired length template. Create an equilateral triangle using a length template 7. Take a rectangular sheet of A4 format, hold it in a horizontal position. 8. Place the length template on the rectangle so that the two lower left corners coincide. 9. Fold the rectangle into a valley, from right to left, resting on the right edge of the template shape. 10. Flip the fold from right to left. We obtain a rectangular shape which has on its left a rectangular flap in a vertical position. 11. Form an oblique valley fold from right to left and top to bottom, passing through the upper left vertex of the upper rectangular flap and its lower right vertex. 12. Open the fold by tilting the right rectangular flap backwards, around the hinge fold. We obtain a rectangular trapezoid whose tip, turned towards the right, carries a triangular flap having a small side located at the top. 13. Bring, through a valley fold resting on the short upper side of the upper triangular flap, the upper horizontal edge on the right hinge side. A triangle is drawn, with one point pointing upwards. At the bottom left, a portion of paper protrudes beyond the lower horizontal edge. 14. Flip the fold from right to left. 15. Fold the protruding part using a valley fold, resting on the lower horizontal edge. 16. Insert the tab that has just been folded inside the fold. 17. Flip the fold from right to left so that you have a smooth side. Here is a fairly magical equilateral triangle construction... |
| Contents | File |
| Equilateral Triangle - PDF file | ML-Orimaths05Ang.pdf |