RF Cafe Software

RF Cascade Workbook 2005 - RF Cafe
RF Cascade Workbook

Calculator Workbook
RF Workbench
Smith Chartâ„¢ for Visio
Smith Chartâ„¢ for Excel
RF & EE Symbols Word
RF Stencils for Visio

About RF Cafe

Kirt Blattenberger - RF Cafe WebmasterCopyright
1996 - 2016
Kirt Blattenberger,

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:

Try Using SEARCH
to Find What You Need. 
There are 1,000s of Pages Indexed on RF Cafe !

Electronics World Cover,TOC,and list of posted Popular Electronics articles QST Radio & TV News Radio-Craft Radio-Electronics Short Wave Craft Wireless World About RF Cafe RF Cafe Homepage RF Cafe in Morse Code Google Search of RF Cafe website Sitemap Electronics Equations Mathematics Equations Equations physics Manufacturers & distributors Engineer Jobs Twitter LinkedIn Crosswords Engineering Humor Kirt's Cogitations Engineering Event Calendar RF Engineering Quizzes AN/MPN-14 Radar 5CCG Notable Quotes App Notes Calculators Education Magazines Software,T-Shirts,Coffee Mugs Articles - submitted by RF Cafe visitors Simulators Technical Writings RF Cafe Archives Test Notes RF Cascade Workbook RF Stencils for Visio Shapes for Word Thank you for visiting RF Cafe!

Drawing a Circle with a Framing Square and 2 Nails

"Squaring the circle" may as yet be an unattainable goal for even the best mathematicians, but the November 2012 edition of The Family Handyman magazine had a tip for how to use a square (of the framing type) and two nails to draw a circle. This is what it said (emphasis added by me):

Make a circle with a square

"Here's a tip for laying out small circles or parts of circles. Tack two nails to set the diameter you want, then rotate a framing square against the nails while you hold a pencil in the corner of the square. You might need to rub a little wax or some other lubricant on the bottom of the square so it slides easily. Don't ask us why this process works; all we know is that it does."Draw a Circle with a Square - The Family Handyman(c), November 2012 - RF Cafe

They're either very honest or they don't think the average reader would understand the explanation.

The Pythagorean theorem is the key, of course, for explaining the reason. For any right triangle:

Pythagorean Theorem in a Circle - RF Cafe   a2 + b2 = c2,

where 'a' and 'b' are the lengths of the two perpendicular sides, and 'c' is the length of the hypotenuse. The same equation also happens to be (not by coincidence) the equation for a circle of radius 'c,' with the center at point (0,0). So, it stands to reason that if all of the parameters are met (three intersecting straight sides with a right angle between two of them), then the locus of points of all permissible value pairs (a,b) will result in a circle. It does not matter whether your value of 'c' represents a radius or a diameter. The hypotenuse will always be the length between the two nails and sides 'a' and 'b' will always be the distance between each nail and the 90° vertex. QED

Audels Carpenters and Builders Guide Cover - RF CafeAudels Carpenters and Builders Guide Cover Page - RF CafeOut of curiosity, I dug out my father's old Audels Carpenters and Builders Guide (printed in 1945) to see if it described the method and if it did, was there an explanation offered. The author did show how to draw a circle with a framing square, and even described how to find the diameter of a circle whose area is equal to the sum of the areas of two given circles (not sure why that would be need by a carpenter). However, an explicit reason for why it all works out is never given.

Here is what is included in the manual:


Audels Carpenter and Builders Guide - Drawing a Circle with a Builder's Square (page 333) - RF Cafe


Audels Carpenter and Builders Guide - Drawing a Circle with a Builder's Square (page 334) - RF Cafe

Audels Carpenter and Builders Guide - Drawing a Circle with a Builder's Square (page 335) - RF Cafe

FIG. 939.-Problem 1: To describe a semi-circle with given diameter.

Outer heel method:

Drive brads at points L, F, extremities of the given diameter. With pencil held at the outer heel M, slide square around with its sides in contact with L, and F, then with the pencil held at M, describe a semi-circle.

Inner heel method:

Obviously if the pencil be held at S, it will be better guided, than at M. In this method, the distance L'F' should be taken to equal diameter, the inner edges of the square sliding on the tacks-the same edges (in either case) that guide the pencil.

At the ends of the diameter LF (fig. 939) drive brads. Place the outer edges of the square against the nails and hold a lead pencil at the outer heel M, any semi-circle can be described as indicated.

This is the outer heel method. but a better guide for the pencil is obtained by the inner heel method also shown in the figure.

FIG. 940 - Problem 2: To find the center of a circle. At the points MS, and LF, where the sides of the square cut the circle when placed in any position with heel in circumference, draw diameter and then intersection will be the center of the circle. Why?

FIG. 941 - Problem 3: To describe a circle through three points not in a straight line. Let L, M, and F, be the given points. Join these points with lines LM, and MF, bisecting them at 1 and 2. Apply square with heel at 1 and 2 as shown and the intersection of perpendiculars thus obtained at S, will be the center of circle which, with radius LS, may be described through LM and F.

To find the center of a circle.

Lay the square on the circle so that its outer heel lies in the circumference. Mark the intersections of the body and tongue with the circumference. A line connecting these two points is a diameter and by drawing another diameter (obtained in the same way) the intersection of the two diameters is the center of the circle as shown in fig. 940.

To describe a circle through three points not in a straight line.

Joint points with straight lines; bisect these lines and at the points of bisection erect perpendiculars with the square. The intersection of these perpendiculars is the center from which a circle may be described through the three points as in fig. 941.

To find the diameter of a circle whose area is equal to the sum of the areas of two given circles.

Let O, and H, be the given circles (drawn with diameters LR, and RF at right angles). Suppose diameter of O, be 3 inches, and diameter of H, 4 inches. Then points L, F, at these distances from the heel of the square will be 5 inches apart as conveniently measured with a two-foot rule as shown. This distance LF, or 5 inches, is diameter of the required circle. Proof: LF2 = LR2 + RF2, that is 52 = 32 + 42 or 25 = 9+16. (this is as close as they come to explaining the phenomenon, but not really)

Posted December 25, 2012

These items are an archive of past Topical Smorgasbord items that have appeared on the RF Cafe homepage. In keeping with the "cafe" genre, these tidbits of information are truly a smorgasbord of topics. They all pertain to topics that are related to the general engineering and science theme of RF Cafe. Note: There is also a huge collection of my 'Factoids' (aka 'Kirt's Cogitations') that might interest you as well.

| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 |