Half Slant Line Research Paper

Half Slant Line

The diagonal division of an oblong (rectangle made from two equal squares) creates unique shapes and angles among the Parquet Tiles; inasmuch as the one by two inch plane is cut across its surface corner-to-corner. <insert image157 here> In making such a cut, the diagonal line passes through the center of the block or plane exactly in the middle, thus the concept of a half slant line. On the other hand, the diagonal division of a single square cut corner-to-corner divides it into two half-squares that together contain four 45° angles, repeated in many Froebel’s Kindergarten exercises. Similarly, the half-slant line also divides two square (right-angle) corners of the rectangle, except that the right-angle corners are divided unequally into two acute angles

However, true 30 degree angles are not introduced as such until the last Parquet Tile, the 120 degree obtuse-angled triangle, which contains two equal 30 degree acute angles. In the case of the right-angled scalene triangle, its significance will be seen in Occupations 3 and 4 (Sewing and Drawing), in which the exercises mimic the diagonal division of the oblong, except that the division occurs on grid paper in the execution of half-slant lines. Just like in the right-angled scalene triangle, the term half-slant line is given to describe a diagonal line that splits an oblong measuring two squares in length exactly in half. Thus, the angles of the forms created in exercises by joining right-angled scalene triangles can be estimated by totaling the number of degrees found in adjacent angles. For instance, by combining two tiles with the short sides or edges touching, form an obtuse-angle