Welcome to Aquarius, Volume 8 (August 16, 2007), ** Squaring the Circle Exactly**.

* Summary of Constructions that accomplish squaring the circle exactly. *(2 pages)

__Introduction to constructions (for beginners)__:

Re-construction of angle

Re-construction of similar triangle

Square root of a value, squaring the rectangle

__The 26 constructions performed to accomplish squaring the circle exactly__:

__The five-sixths constructions__:

__Construction #1__ (tan=2)

--->(to get 1, 1/5, 1/6 and 5/6 values, together with Construction #2)

__Construction #2__ (tan=2)

--->(to get 1, 1/5, 1/6 and 5/6 values, together with Construction #1)

__Construction #3__ (tan = 5/6) --->[to get (5/6) and (6/5) and other helpful values]

__The nine-elevenths constructions__:

__Construction #4__ (tan= 9/11) --->[ to get (9/11) and (11/9)]

__The point fifty-five constructions__:

__Construction #5__ (tan= 0.55) --->(to get 0.55 value)

__Construction #6__ (tan= 0.45) --->(to get 0.45 value)

__The 36-54 rt tri, the 18-72 rt tri__:

__Construction #7__ --->(Construction of the 72-degree angle)

__Construction #8__ --->(Construction of the 18-72 degree right triangle)

__Dividing line, new constructions specifically required to square the circle follow__:

__The (secant 18)^4 constructions__:

__Construction #9__ --->[to get line length 1.222291236..., (secant 18)^4]

__Construction #10__ --->(to get 7.778, and 2.222, 0.7778 and 0.2222)

Study of the next section, *The Definition of MQ*, is strongly recommended in order for the reader to understand the purpose of the constructions that follow.

__Construction of TN and NT__:

__Construction #11-1, 11-2__ --->(Construction of TN and NT in two steps)

__Construction of MQ and M__: [Constructions #12, 13, 14, 15, 16]

__Construction #12__ --->(six steps, to get NTP value [0.999937891...])

__Construction #13__ --->(to get tangent = 1.222291236...)

__Construction #14__ --->( to get 1.22221532123408073944164930824006... [MQ+0.2222])

__Construction #15__ --->(final construction to get MQ), simple line constructions on page

__Construction #16__ (square the rectangle, by reference to this procedure)

__The Get Pi constructions__:

__Construction #17-1__ --->(to get ratio of 1.618033989...)

__Construction #17-2__ --->(to get line length of Phi^2)

__Construction #18__ --->(to get tangent = [Pi*(5/6)] )

__Construction #19__ --->(to get line length [Pi*(5/6)] )

__Construction #20__ --->(in two steps, to get line length of Pi)

__The Pi and 1 constructions (copy from Volume 1)__:

(21) PM constructions [(Pi/2-1) is cosine]

(22) RP construction [(Square Root of Pi)/2 is cosine]

(23) OR construction [1/sqrt(Pi) is cosine]

(24) RE construction [1/sqrt(Pi) is length of Base]

(25) Square to Circle (STC)

(26) Circle to Square (CTS)

__The Pi and MQ constructions__ --->(alternative square = circle area, text and equations)

Link to: (Welcome) or (Geometry Alpha Index).