The Dialectical Opposition Between Rectilinearity versus Curvilinearity in Geometries.

  

The Dialectical Opposition Between Rectilinearity versus Curvilinearity in Geometries.

 

 

 

 

 

 

Dear Reader,

 

 

This blog-entry is to share, with you, a recent new Encyclopedia Dialectica ‘dialectogram’, presenting the systematic dialectic of the mathematical – geometrical -- categories of ‘rectilinearities versus curvilinearities’, posted above.  Note the 2-scales, finitary 'qualo-fractality' of that 'dialectogram'.

 

Perhaps the most interesting, most valuable aspect of this dialectic, is not the ‘categorial antithesis’, R ~ C, or, q_R ~ q_C, just stated above, but its ‘categorial synthesis’, q_CR.

 

The sub¹-species of that q_CR [sub⁰-]species represent some of the most important developments in the ancient-to-modern history of mathematics.

 

These include the derivation of the so-called “transcendental irrational” number, p, as the ‘reconciliator’ of the rectilinear Diameter of an ideal, “perfect” circle, with the curvilinear Circumference of such a circle:  p = C/D.

 

These also include the “differentiation operation” of the “differential calculus”, e.g., the limit of the ratio of the function-value, f(t + Dt) of a function, f, as Dt goes to[ward] 0, to its “argument” ‘augmentor’, (Dt) –

 

lim_(t ® 0)(Df(t+Dt)/(Dt))    ®    df(t)/dt

 

-- the latter, df(t)/dt, the “differential coefficient’, as the ‘reconciliator’ of the f(t) curve with the line of slope df(t)/dt, the [rectilinear] ideal tangent line, intersecting the ideal curvilinear locus of f(t), as t varies widely, but, for a given, specific value of t, representing that tangent line at only a single, ideal “point” of the f(t) curve, with the coordinates (t, f(t)).  

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, please see --

 

www.dialectics.info

 

 

 

 

 

 

 

 

For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ – as well as dialectically-illustrated books published by the F.E.D. Press, see –

 

https://www.etsy.com/shop/DialecticsMATH

 

 

 

 

 

 

 

¡ENJOY!

 

 

 

 

 

 

 

Regards,

 

 

Miguel Detonacciones,

 

Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];

Elected Member, F.E.D. General Council;

Participant, F.E.D. Special Council for Public Liaison;

Officer, F.E.D. Office of Public Liaison.

 

 

 

 

 

 

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