US2534601A

US2534601A - Triangle calculator

Info

Publication number: US2534601A
Application number: US99790A
Authority: US
Inventors: Willard H Jensen
Original assignee: Individual
Current assignee: Individual
Priority date: 1949-06-17
Filing date: 1949-06-17
Publication date: 1950-12-19
Anticipated expiration: 1967-12-19

Description

Dec. 19, 1950 Filed June 17, 1949 W. H. JENSEN TRIANGLE CALCULATOR 3 Sheets-Sheet 1 I N VE N TOR.

W/LL FROMIENSE/V,

BY 2444M Dec. 19, 1950 w, H, JENSEN I 2,534,601

TRIANGLE CALCULATOR Filed June 17,1949 3 Sheets-Sheet 2 Patented Dec. 19, 1950 UNITED STATES. PATENT OFFICE TRIANGLE CALCULATOR Willard H. Jensen, Longview, Tex.

Application June 17,1949, Serial No. 99,790

s 4 Claims.

This invention relates to calculators for aiding in the solution of trigonometric problems.

The primary object of the invention is to provide a simple mechanical calculator for solving triangles.

A more specific object of the invention is to provide a mechanical calculator which is capable of assisting in the solving for unknown values of both right and oblique triangles.

With the foregoing and other objects in mind, the invention resides in the following specification and appended claims, certain embodiments and details of construction of which are shown in the drawings in which:

Figure 1 is a plan view of the calculator,

Figure 2 is a plan view of the opposite side of the calculator from Figure 1,

Figure 3 is a View in side elevation of Figure 1,

Figure 4 is a view in side elevation of Figure 2, and

Figures 5, 6, 7, 8 and. 9 are segmental Views'of rotatable disk members used in the calculator.

Referring more particularly to Figures 1 and 3 a pair of circular plates I and 2 are shown suitably spaced apart by spacers 3. The plates are preferably made of opaque plastic, although other material such as wood or metal would be satisfactory for the purpose. Inscribed on the surface of plate I is a right triangle 4 having

sides

5, 6 and I and complementary angles D and E. Within the complementary angles of the triangle are windows 8 and 9 in plate I. Associated with

sides

5, 6 and- I are windows I 0, II and I2 respectively provided in plate I. Inscribed in the surface of the plate among the

windows

5, 6 and l are indicia of multiplication, division and directions for instructing the user of the calculator as will be set forth later in the specification.

Adjacent to the under side of plate I are toothed disks I3, I4, I and I6 rotatably mounted on pivots II, I8, I3 and 20 respectively. The teeth on disk I5, which is the operating disk, mesh with teeth on disks I 6 and I4. The teeth on disk I4 also mesh with the teeth on disk I3. A portion of the periphery of disk'l5 extends beyond the periphery of plate I at 2| to facilitate manual movement of disk I5. This disk is provided with 50 teeth and has indicia representing angles from 1 to. 45 degrees as shown in Figure 5. Disk I4,

shown partially in Figure '7, is also provided with 50 teeth and has indicia representing the co-sine and co-tangent functions of those angles on disk 15. Disk I3, shown partially in Figure 9, is provided with 50 teeth and with indicia representing the trigonometric functions of tangent and the side 6 be one inch for example.

sine of angles on disk I5. The disk I6 is partially shown in Figure 8 and is inscribed with indicia representing the trigonometric functions of sine and co-sine of angles appearing on disk I5.

The operation of the calculator now becomes readily apparent. For example, under a given condition of one known complementary angle and one side the other two sides may be readily determined by following the direction indicia on plate I. Thus move disk I5 until the angle of 15 degrees (as shown) appears in window 9. Disks I3, I4 and it are automatically moved to present trigonometric function values of the angle 15 degrees in windows II], II and I2. Let Then to solve for side 5, it is merely necessar to follow the directing indicia arrow from side 6 to side 5 and multiply side 6 by the function appearing in window III which is .2679 or the tangent of 15 degrees. Thus since side 6 is one inch, the value of side 5 is .2679-inch.

Other calculations are as easily determined. Assume the angle 15 degrees is given along with side I; the problem being to find side 5. Follow the directing arrow indicia from side I to side 5 and multiply by the function appearing in win dow II] or .2588 which is the sine of 15 degrees. Thus if the length of side I is one foot the length of side 5 is .2588 foot.

To find side I with the same given angle of 15 degrees and side 5 known at 10 feet, follow the directing arrow indicia from side 5 to side I and do what the indicia says-namely, divide side 5 by the function .2588 appearing in window I2 which is the sine of 15. degrees. In other words, divide 10 feet by .2588 to arrive at the length of side I.

If the angle E is given it is merely necessary to move disk I5 until this angle appears in window 8 at'which point the complementary angle D appears in window 9 and the procedure is the same as in the above examples.

Referring now to Figures 2, 4 and 6 the plate 2 is shown having inscribed thereon an oblique triangle 22 having sides 23, 24 and 25. Within each angle of the triangle are

windows

26, 2! and 28 in plate 2. Also within the triangle and associated with'the angle windows are windows 29, 20 and 3| in plate 2. Indicia similar to that used on plate I are used to direct calculations.

Adjacent the under side of plate 2 are identical

rotatable disks

32, 33 and 34 suitably mounted on pivots 35, 36 and 31. The peripheries of these disks extend beyond the peripher of plate 2 to ease the manipulation of same. The disks are each provided with indicia of angles and sine functions as shown partially in Figure 6.

The plate 2 of the calculator can assist in solving any oblique triangles having 2 angles and 1 side given, or by merely following the suitable trigonometric formulae which may be inscribed on the plate 2 for solving oblique triangles where two sides and the included angle are given.

Calculations are made as follows:

To find side 24 with the angles D and E and side 2e given, follow the directing arrow from side 2s to window 3! and multiply (as directed by the indicia) side 25 by the function in window 5|. Continue to follow the directing arrow from window 3i to window 29 and use the sign given. Thus divide the product obtained from multiplying side 25 by the function in window 3! by the function in window 29, the result being the length of side 24.

To find side 23, side 24 and angles F and D being given, set the disks so that the correct angles appear in windows 27 and 28. Set disk so that the difference between 180 degrees and the sum of angles D and F appears in window 26. Proceed from the given side 24 following the arrows to the window 30 and multiply (as directed by the indicia) side 24 by the function in window 39. Then follow the ar rows directly to window 3| and divide the product of side 24 and the function in window 35 by the function in window 3|, the result being the length of side 23.

To solve triangles having one angle greater than 90 degrees, it is merely necessary to subtract the given angle from 179 degrees and use the function for the resulting remainder, proceeding in calculations as above.

Thus it is seen that the calculator presented by the invention, which is simple to use, economical to manufacture as well as being accurate in computations, precludes the use of trigonometric tables in the solvin of triangles.

I claim;

1. A calculator for solving triangles comprising a pair of spaced plates, one side of said plates having a geometric representation thereon of a right triangle, the other of said plates having thereon a geometric representation of an oblique triangle, a plurality of windows in the plate with the oblique triangle, said windows being positioned adjacent each angle of the triangle, a plurality of windows in the plate with the right triangle, said windows being positioned adjacent each side and each of the complementary angles of the right triangle, a system of intermeshing disks rotatably mounted between the plates and adjacent the right triangle plate, a series of independent disks rotatably mounted between said plates and adjacent the oblique triangle plate, and indicia representing trigonometric functions and angles on the disks, the said disks being movable to present the proper related indicia before each window to assist in the solving of the unknown angle and side values of the triangles when certain of such values are known.

2. A calculator for solving triangles comprising a pair of spaced circular plates, one of said plates having a geometric representation inscribed thereon of a right triangle, the other of said plates having inscribed thereon a geometric representation of an oblique triangle, a plurality of windows in the plate with the oblique triangle, said windows being positioned ad acent each angle of the triangle, a plurality of windows in the plate with the right triangle, said windows being positioned adjacent each side and each of the complementary angles of the right triangle, a driving disk and three driven follower disks rotatably mounted between the plates and adjacent the right triangle plate, the driving disk having its periphery extending beyond the peripheries of the plates, a series of independent disks rotatably mounted between said plates and adjacent the oblique triangle plate, the peripheries of the disks extending beyond the peripheries of the plates, and trigonometric function indicia on said rotatable disks for selective presentation to the plate windows to assist in the solving of the unknown angle and side values of the triangle when certain of such values are known.

3. A calculator for solving triangles comprising a plate, a geometric representation of a right triangle inscribed on said plate, windows in the plate associated with the complementary angles of the inscribed triangle and with the three sides of said triangle, rotatable disk means to present a given angle in one of the complementary angle windows and follower disks driven by said disk means to automatically present the complementary angle of the given angle in the other angle window and the trigonometric functions of such given and complementary angles in the windows associated with the sides of the inscribed triangle.

4. A calculator for solving triangles comprising a plate, a geometric representation of a right triangle inscribed on said plate, windows in the plate associated with the complementary angles of the inscribed triangle and with the three sides of said triangle, rotatable disk means to present a given angle in one of the complementary angle windows and follower disks driven by said disk means to automatically present the complementary angle of the given angle in the other angle window and the trigonometric functions of such given and complementary angles in the windows associated with the sides of the inscribed triangle and multiplication, division and direction indicia associated with said windows presenting the functions to visually instruct the user in using the functions to determine the unknown sides of a triangle.

WILLARD H. JENSEN.

REFERENCES CITED The following references are of record in the file of this patent:

' UNITED STATES PATENTS