Squaring the Circle 396 x 8 = 3168
This page ventures into an ancient puzzle, squaring the circle, and a curious numeric thread: 396 × 8 = 3168.
I claim no mastery, only a persistent wonder and a joy in tracing the patterns that shimmer through numbers.
Numbers are the breath of creation. They carve the world into spirals and symmetries—seen in petals,
felt in orbits—while resonating in scripture with divine clarity. Geometry is the visible echo of numbers,
and squaring the circle is one of its oldest melodies.
The Ancient Quest
To square the circle is to craft a square with the same area as a given circle using only a compass and
straightedge—an elegant impossibility, as π’s infinite nature defies such precision. Yet the pursuit reveals
more than its failure. A dance between the finite and the infinite, a riddle etched into the fabric of thought.
A Numeric Whisper: 396 × 8 = 3168
Echoes in Scripture and Shape
This number, 3168, ripples beyond math. In biblical numerology, some tie it to the Greek name of Jesus
—ΙΗΣΟΥΣ (Iesous)—whose gematria value is 888, a multiple of 8. And 3168 feels circular: a circle with
circumference 3168 units has a diameter near 1008 (since C = πd, d ≈ 3168 ÷ 3.14159 ≈ 1008), a number
hinting at completion. Scripture sings of such order: “He has measured the waters in the hollow of His
hand” (Isaiah 40:12). Could 396 × 8 be a shadow of that measure, squaring the circle in symbol if not in proof?
This isn’t a solution—it’s a spark, a glimpse of connection. I offer it freely for you to ponder, test, or reshape.
Numbers are bridges—linking us to creation, to each other, to the divine. May this stir your imagination and
light a path through the mystery.
I experimented with the interesting numbers 3-6-9, and 396 became the diameter for a circle.
Of course, now that the technique is known, any circle diameter will do.
The square area in my experiment: (a-b 2772 mm x 2) 2 = 30735936.
My circle radius result: 3127.86697555..., with an area of 30735934.51364089...
I managed an accuracy of at least 99.999995... %
Place 8 circles along the X-axis and 2.5 on the Y-axis, and add guide-line A.
Connect a line starting from b (diagram 1) to c (on the Y-axis), touching the circle at "e"
as accurately as possible. Important! The accuracy of the final result depends on it.
Draw the line e-f parallel to the X-axis, and circle radius o-f.
Draw circle 1 (radius u-o), then 2, then add guide line B.
Circle radius q-m as shown (q = B guide line and circle). It produces point h, and the inner circle.
Circle radius o-h and draw guide line C through point i.
Intersection of guide lines C and A is z.
Draw line b-z = the circle radius.
Circle area (radius b-z) 2 x π should closely match Square area (line a-b x 2) 2
Doing this by compass and pencil one can get a quite accurate result,
by drawing the C guide line just below the top of the upper circle.
There are a few variation possibilities to this construction method.
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Lastly, a less accurate but easier and fun construction method where (A-D)2 + (D-B)2 = (A-B)2 :
1. Draw circles 1, 2, 3
2. Draw triangle and post.
3. Draw guide lines as shown.
Circle radius A-B = √10 000 000 mm. Area = π x 10 000 000 (31415926.535... mm)
A-C = 2800 mm, and a square area of (2800 x 2) 2 = 31360000 mm
Accurate to 99.9%