1934NIPPON SUISAN GAKKAISHIOpen access

The Equation of the Form of a Bowl-shaped Net and the Forming of it with Rectangular Pieces of Net only

Hideaki Miyamoto

Open full text 0 citations

Abstract

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).

Open-access reader

About this research paper

What this paper is about

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).

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

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)

Related papers

Back to paper searchBrowse research topicsOriginal source
The Equation of the Form of a Bowl-shaped Net and the Forming of it with Rectangular Pieces of Net only — Research Paper | ScholarLens