The circumference of the circle intersecting the unique (x/6)⁴/x³ = 8x³/x⁴ absolute dead center cube hyperbola

1 See, on this web, Theorem & Proof: The Uniqueness of the Absolute Dead Center Cube.  Cf. D.G. Leahy, The Cube Unlike All Others (CreateSpace, 2010), Section I.1.  The operation here described uniquely shared by real trinary logic and the absolute dead center cube at once logically differentiates the dead body and the living body.  Cf. D.G. Leahy, Beyond Sovereignty: A New Global Ethics and Morality (Aurora, 2010), pp. 63f., n. 14: “What is required [to understand the logic of ‘the body qua living’] is that the mediated identification be qua actual an existing root of the whole. The members of the living body qua actual β = {{}{00}} and qua actual reciprocal interrelatedness γ = {{01}{01}} and δ = {{1}{1}} are embodied members of the body immediately qua actual the whole and an existing root of the whole α = {{}{00}} = {{{01}{01}}{{1}{1}}} = {11} = {1} that is the body. Each embodied member of the living body qua actual and qua actual reciprocal constitutional interrelatedness is identically the set of logical elements that are their square roots α = {1}.”  The integral product of τό σῶμα τῆς ζωῆς, ‘the body of life’, = 6.5028096e25 (where 65028096 = 1 × 784 × 82944 the product of the three natural numbers uniquely equal to their integral products.  See, below, n. 4), the rational product = 112.5 (= 1.13⁻¹ × 2⁷), and the linear product = 5.7802752e23.  5.7802752e23^.125 ≈ 3.2e5/343 the rational product, the ‘identity’, of Λόγος καὶ ἀριθμός, ‘logos at once number’.  So, also, (5.7802752e23^.125)^17/37 [≈ (3.2e5/343)^17/37] ≈ e^π = (−1)^-i.  See, below, n. 10.

2 Adapted from S-B. Liao, et al., “Introduction to Electricity and Magnetism”, MIT OpenCourseWare.  Online.  Available at: http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/maxwells-equations/the-displacement-current-and-maxwells-equations/MIT8_02SC_notes26to30.pdf.  February 2013.  For the occurrence of visible electromagnetic light waves in the early universe, see, on this web, The Light, the Logic, & the Inhomogeneities.

3  Ibid.

4 See, on this web, Measure Beyond Beyond Reach.

5 For the capacitor illustration and the Poynting vector equation following, cf., above, n. 2, S-B. Liao, et al.  √10368 is the unit dimension of the edge of the absolute dead center cube (cf., above, n. 1).

6 Where M = mass, M/T = mass flow rate, M/T² = surface tension, and M/T³ = the Poynting vector, consider the sequence M, M/T, M/T², M/T³ where the following is true (M × M/T × M/T²)/M/T³ = M².  Note also that where i(x) is the integral product of x, and i(x) = x, and i[i(x)/3] = i(x)/9, then, uniquely among all natural numbers, x = 82944 (cf. D.G. Leahy, Foundation: Matter the Body Itself [Albany, 1996; eBook, 2009], Sections III.6 and IV.2, et passim; also, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms).  Then let there be the sequence [i(x)/9]/i[i(x)/9], i(x)/9, i(x), corresponding by analogy to the first three members of the stipulated M sequence, where [i(x)/9]/i[i(x)/9] = 113.7̅7̅7 = 32² × 9⁻¹ (corresponding to M mass), i(x)/9 = 9216 = 32² × 9¹ (corresponding to M/T mass flow rate), and i(x) = 82944 = 32² × 9² (corresponding to M/T² surface tension).  The question arises what/where is the 4^th term corresponding to the Poynting vector M/T³ in the stipulated M sequence?  The 4^th term turns out to be i[i(x)/9][i(x)] = 6718464 = 32² × 9⁴ (corresponding to the M/T³ Poynting vector), where 6718464 = (36√2)⁴ = r⁴ = the inradius (the radius of the inscribed circle) of the face of the absolute dead center cube raised to the 4^th power, neatly corresponding geometrically to the 4^th power of the radius of the charging capacitor circular parallel plates, R⁴, in the Poynting vector equation:

 .

Note that the rightness of the analogy is further demonstrated in the fact that as (M × M/T × M/T²)/(M/T³) = M², so ([i(x)/9]/i[i(x)/9] × i(x)/9 × i[x])/(i[i(x)/9][i(x)]) = ([i(x)/9]/i[i(x)/9])².  For more on the inradius of the absolute dead center cube, cf., below, n. 10; also, on this web, The Diagonal Logic of the Triple Absolute Dead Center Cube & Certain Fundamental Mathematical & Physical Constants.  Cf., also, on this web, Absolute Particularity: Beyond the Problem of Universals.

⁷ Cf. Leahy, Foundation, Section III.1, et passim.  See also, on this web, Quantum Gravitational vs. Quantum Logic: Virtually Left-handed Real Trinary Logic.  Cf., also, D.G. Leahy, Faith and Philosophy: The Historical Impact (Aldershot and Burlington, 2003), Chapter 7.

⁸ Cf., above, note 1, and Leahy, Foundation, Section III.5, et passim.

⁹ See, on this web, Transdecimal Calculation of Number Identity: A Note on Integral Product & Related Terms.

¹⁰ The complete transdecimal results for the two terms are as follows.  Λόγος καὶ ἀριθμός: Integral product = 8.2944e22, Rational product = 3.2e5/343, Linear product = 8.89056e19.  נקדת האפס של תנופה: Integral product = 8.2944e22, Rational product = 1, Linear product = 8.2944e22.  With respect to the rational product of Λόγος καὶ ἀριθμός, note that (3.2e5/343)^17/37 ≈ e^π = (−1)^-i.  Most precisely,

accurate to .037 ppb, where the difference equals precisely

,

where 2880000 = √8.2944e12 the square root of the integral product of מלה מיד אמצע (‘absolute’ ‘Logos At Once Mean’).   Also, where the inradius of the face of the absolute dead center cube = 36√2, the rational product × the linear product of Λόγος καὶ ἀριθμός = (3.2e5/343) × 8.89056e19 = 3.2e19 × (36√2)² (for more on the role of the inradius of the absolute dead center cube, cf., above, n. 6).  See, also, on this web, The Diagonal Logic of the Triple Absolute Dead Center Cube & Certain Fundamental Mathematical & Physical Constants and Real Trinary Logic, the Imaginary Number i, & the Cyclic Series of Complex Numbers.