Method for using three-dimensional graph

Abstract

To provide a 3D CAD and spreadsheet software which allow for understanding a phenomenon by quantizing the phenomenon and making the phenomenon three-dimensional and allow for deepening understanding of a more abstruse and complicated phenomenon.SOLUTION: A method for displaying a three-dimensional graph includes drawing a circle with a radius R with an origin O as a center in a plane including an X axis and a Y axis of Cartesian coordinates, setting a point Op (0, 0, p) and equally dividing the circle and a segment from the origin O to the point Op by N, and properly setting N, p, and r. When an n-th measured value is denoted as Kn, coordinates (r.Kn.cos(2π.n / N), r.Kn.sin(2π.n / N), p.n / N) of arbitrary data Dn to be inputted are calculated by spreadsheet software, and the data is read in. When a point adjacent to the point Dn is denoted as a point D(n+1) and an N-th point from the point Dn is denoted as D(n+N) and a point having coordinates (0,0,p.n / N) is denoted as On, a segment from On to Dn, a segment from Dn to D(n+1), and a segment from Dn to D(n+N) are automatically plotted.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The present invention relates to cubic graphs. [Background technology]

[0002] I own the rights to Japanese Patent Registration No. 5992740. However, in the past 10 years, there has only been a low-level implementation by a public institution in the United States at the end of last year, namely Non-Patent Document 1. It seems to have been well received on social media, but there have been no reports of any further developments since then. People do not realize that this invention can be used in other fields. As a remedy, this invention will be used in the field of mathematics to prove that it is superior to two-dimensional graphs, and as a side effect, to enlighten people that mathematics is interesting. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2014-010727 [Non-patent literature]

[0004] [Non-Patent Document 1] Authors & editors: Robert Nemiroff (MTU) & Jerry Bonnell (UMCP), “Astronomy Picture of the Day”, [online], August 22, 2022, NASA Official: Philip Newman. Specific rights apply. Retrieved April 29, 2024. Internet.<URL:https: / / apod.nasa.gov / apod / ap220822.html>

[0005] [Non-patent document 2] Edited by Ryuji Matsumoto, "Pi Formula Collection", [online], August 14, 2021, searched April 29, 2024, Internet,<URL:http: / / www.pluto.ai.kyutech.ac.jp / ~matumoto / dvi / pi.pdf> Summary of the Invention [Problem to be solved by the invention]

[0006] The problem it seeks to solve is that the patent is only recognized as a graph showing global warming. [Means for solving the problem]

[0007] The present invention aims to quantify and three-dimensionalize phenomena and understand them by implementing the above patents. [Effects of the Invention]

[0008] The present invention provides a better understanding of a complex and difficult phenomenon. [Brief explanation of the drawings]

[0009] [Figure 1] Figure 1 shows the coordinates used in this study input and output using 3D CAD and the aforementioned patent. [Figure 2] Figure 2 shows the output of Figure 1 after inputting unit 1. [Figure 3] Figure 3 shows Table 2 drawn using 3D CAD. [Figure 4] FIG. 4 is an explanatory diagram of another method for determining Dn. [Figure 5] Figure 5 is a view from arrow A in Figure 3. [Figure 6] This is an enlarged view of the convergence value as viewed from the arrow B when it is assumed to be cylindrical and is superimposed on Figures 3 and 5. [Figure 7] Figure 7 is a plan view of Figure 6 created using 2D CAD. [Figure 8] FIG. 8 is an enlarged view of part C in FIG. DETAILED DESCRIPTION OF THE INVENTION

[0010] People currently use two-dimensional graphs to capture phenomena. Some of them have 3D functions, but the coordinates are vague and difficult to understand. My aforementioned patent solved this problem, but it has been going strong for the past 10 years, and only last year did it become available as a low-dimensional implementation non-patent document 1. People don't really understand. Therefore, this time we will use pi as an example to help you understand the validity of the above patent. As a side effect, it also showcases the fun of mathematics. [Example]

[0011]

number

[0012] According to Non-Patent Document 2, Mathematical Formula 1 was discovered by James Gregory (1638-1675) in 1671. However, it seems to converge slowly and is not suitable for practical calculations.

[0013] [Table 1] TIFF2025177122000004.tif1239TIFF2025177122000005.tif7070TIFF2025177122000006.tif5174

[0014] Table 1 shows the numerical results of Equation 1, which were converted using Microsoft Excel. Indeed, even if you calculate up to the last line of the spreadsheet, that is, n=1,048,574, the results only match up to five decimal places. Convergence is slow.

[0015] Figure 1 shows the coordinate system used in this study. A circle with a radius of r and a point O with coordinates (0,0,p) in the Z direction is located on a plane containing the X and Y axes of the Cartesian coordinate system. p and the line segment O·O p It consists of:

[0016] Figure 2 shows Figure 1 with N=8, p=r=1, and a unit of 1. The circle in Figure 1 is divided into eight equal parts, and the height is changed to 0, p / 8, p / 4, . . . ., p at intervals of 0, π / 4, π / 2, . . ., 2π (rad). This results in the spiral lines shown. While the circle was divided into eight equal parts in this example, it is also possible to divide it equally by a natural number, N. In this case, the Z coordinate is changed to 0, p / N, 2p / N, 3p / N, . . ., p. However, if N is 1 or 2, the result will not be three-dimensional. For data like Table 1, which alternates between positive and negative values, an even number is preferable. Finally, while it is theoretically possible for N to be a real number satisfying N ≠ 0, this is not suitable for three-dimensional graphing. Note that N, r, and p must be set. In this example, N=8, r=p=1.

[0017] [Table 2]

[0018] Table 2 shows an excerpt from Table 1 with the calculated X, Y, and Z coordinates. First, the Z coordinate is calculated as p·n / N. The measured value of n is n Then, the Y coordinate is r·K n ·sin(2 π·n / N), X coordinate is r·K n ·cos(2π·n / N).

[0019] Figure 3 shows the output obtained by inputting the data in Table 2 using the coordinates in Figure 1. I used Google Sketch Up, but it doesn't have the function to read X, Y, and Z coordinates from a spreadsheet, so I had to input them manually. However, the 2D software I'll explain later uses a certain method to read X and Y coordinates. So, I'll explain it assuming that this function has been added. First, I'll take any data D n , n measurement value K n Then D n is the coordinate (r K n cos(2π n / N),r K n sin(2π·n / N),p·n / N). Although it would be possible to display and output only this, we decided that this is not suitable for the purpose of this study, and so we will use point O n Load (0,0,p·n / N) and use the line segment O n D n Then create point D n The point adjacent to D (n+1) Let D be the line segment n D (n+1) Create the final D n The Nth point is then converted to point D (n+N) Let D be the line segment n D (n+N) is created and output.

[0020] Up to this point, we have reviewed Patent Document 1. The expressions were poor and sometimes difficult to understand, so we have organized them. Next, point D n I noticed that there is another way to calculate the input. As shown in Figure 4, point D n Azimuth angle α n , elevation angle β n , distance L Kn This calculation is shown in the following equation 2.

[0021]

number

[0022] The calculation of equation 2 can be easily done with a spreadsheet. The advantage of this calculation method is that it is possible to calculate the distance from one point at the origin O to point D. n can be found. Point Dn Once this is found, you can draw it in the same way as described above.

[0023] FIG. 5 is a view taken along the arrow A in FIG.

[0024] As n gets larger, you can see how it converges to a certain value. It's a beautiful sight.

[0025] Figure 6 shows an enlarged view of Figures 3 and 5 superimposed on each other, assuming that the convergence value is cylindrical. You will notice that the line connecting adjacent data points will always intersect with the convergence value at one point. The reason we assumed it to be cylindrical is that although we divided a plane circle containing the X and Y axes into eight equal parts in this example, if we divide it into a larger number of equal parts, it will converge to a circle.

[0026] The 3D software used to create Figure 5 cannot create accurate floor plans. Therefore, we used [Jw_cad] developed by Jiro Shimizu & Yoshifumi Tanaka. Figure 7 shows the result created and output using this 2D CAD. The 2D CAD is convenient because it allows data to be read by pasting data from a spreadsheet into a notepad. However, since it is 2D, it can only read X and Y coordinates.

[0027] Figure 8 shows the details of part C in Figure 7. In Figure 8, adjacent data are represented by point D n , point D(n+1), and the bisection point of the line segment Dn·D(n+1) is point Fn. Also, ∠D in Figure 7 n O.D. (n+1) Let the bisector of be the line E. Point D n , point D (n+1) The amplitude between G and the line E and point F n Using our eyes, we can understand that if the distance between G and H is H, then G>H.

[0028] [Table 3]

[0029] For verification purposes, the calculations were carried out using the spreadsheet software mentioned above, and the output is shown in Table 3. Therefore, it was found that the following equation 3 holds true. Math 3 converges faster than math 1.

[0030]

number

[0031] It is unclear whether number 3 is a new discovery, but it does not appear on the web. [Industrial Applicability]

[0032] In this embodiment, the phenomenon is quantified and organized using spreadsheet software, and the 3D CAD reads the data from the spreadsheet software using the coordinates, allowing the phenomenon to be visually understood by inputting and outputting. Next, if it is output using a 3D printer, it will be possible to recognize it not only visually but also tactilely. [Explanation of symbols]

[0033] n: a natural number including 0 O:Origin r: real number (r≠0) p: real number (p≠0) O p : Point with coordinates (0,0,p) N: a natural number greater than or equal to 3 K n :n measurement value D n : Coordinates (r·K n cos(2π n / N), r K n ·sin(2π·n / N),p·n / N) D (n+1) :Point D n and adjacent data O n: Any data with coordinates (0,0,p·n / N) D (n+N) :Point D n The Nth data α n :Azimuth (rad) β n :Elevation angle (rad) L Kn :Origin O to point D n Distance to A→: Look in the direction of the arrow from point A. B→: Look in the direction of the arrow from point B. C: The area surrounded by the square in Figure 7. E: In Figure 7, ∠D n O.D. (n+1) The dividing line F n : Line segment D n D (n+1) Bisection point of G: Point D n and point D (n+1) The amplitude of H: Line E and point F n Distance

Claims

1. In a method for displaying a three-dimensional graph using computer software, a circle with a radius r and a center point O is drawn on a plane containing the X and Y axes of the Cartesian coordinate system, and the point O is p Set (0,0,p) and the circle and line segment O・O p is divided into N equal parts and N, p, and r are set appropriately. The nth measurement value is K n If so, any input data D n Coordinates of (r・K n ・cos(2π・n / N), r・K n ・sin(2π・n / N),p・n / N) can be calculated using a spreadsheet software, and the data can be read in. n The adjacent point is point D (n+1)、 point D n The Nth point from point D (n+N) and the point with coordinates (0,0,p・n / N) is O n Then, the line segment O n, ・D n and line segment D ｎ ・D (n+1) and line segment D ｎ ・D (n+N) 3D CAD that automatically draws.

2. In claim 1, the input data D n The azimuth angle is α ｎ , the elevation angle is β ｎ , distance L Kn This is a 3D CAD that can read calculated values ​​using Equation 2.

3. 3. The spreadsheet software according to claim 1 or 2, characterized in that the spreadsheet software has a 3D CAD function.

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