The Equation of the Form of a Bowl-shaped Net and the Forming of it with Rectangular Pieces of Net only
Hideaki Miyamoto
Abstract
Open-access reader
Hideaki Miyamoto
Abstract
Open-access reader
If a piece of net is set to spread over a square frame with a suitable dip and with the angles between the arms of knots properly adjusted at every point on the frame, a bowl-shaped net is obtained with no crease whatever. In the present paper the form of thus prepared net is surveyed and the forming of a bowl-shaped net with rectangular pieces of net only is given, with the results summarized as follows: - (1) When two lines through the centre of the upper side of frame and parallel to two lateral sides of it respectively are chosen as x- and y- axes, the depth of the net, z, at any point (x, y) is represented by z/z0=[1-4(x/a)2]p[1-4(y/a)2]q where z0 is the depth of net at the centre of the upper side of frame, a the inner dimension of it, and p and q certain constants (1 (a) and 3 in the text figure). (2) The bowl-shaped net of any size, therefore, can be formed with suitable rectangular pieces of net (2, 4 (a, b) and 5(a, b) in the text figure).
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If a piece of net is set to spread over a square frame with a suitable dip and with the angles between the arms of knots properly adjusted at every point on the frame, a bowl-shaped net is obtained with no crease whatever. In the present paper the form of thus prepared net is surveyed and the forming of a bowl-shaped net with rectangular pieces of net only is given, with the results summarized as follows: - (1) When two lines through the centre of the upper side of frame and parallel to two lateral sides of it respectively are chosen as x- and y- axes, the depth of the net, z, at any point (x, y) is represented by z/z0=[1-4(x/a)2]p[1-4(y/a)2]q where z0 is the depth of net at the centre of the upper side of frame, a the inner dimension of it, and p and q certain constants (1 (a) and 3 in the text figure). (2) The bowl-shaped net of any size, therefore, can be formed with suitable rectangular pieces of net (2, 4 (a, b) and 5(a, b) in the text figure).
Key concepts: Net (polyhedron), Point (geometry), Frame (networking), Geometry, Mathematics, Dimension (graph theory), Combinatorics, Square (algebra)