- #1

AntonVrba

- 92

- 0

Rv=

3.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067030299699450949989524788116555120943736485280932319023055820679748201010846749232650153123432669033228866506722546689218379712270471316603678615880190499865373798593894676503475065760507566183481296061009476021871903250831458295239598329977898245082887144638329173472241639845878553976679580638183536661108431737808943783161020883055249016700235207111442886959909563657970871684980728994932964842830207864086039887386975375823173178313959929830078387028770539133695633121037072640192491067682311992883756411414220167427521023729942708310598984594759876642888977961478379583902288548529035760338528080643819723446610596897228728652641538226646984200211954841552784411812865345070351916500166892944154808460712771439997629268346295774383618951101271486387469765459824517885509753790138806649619119622229571105552429237231921977382625616314688420328537166829386496119170497388363954959381457576718533736331259108996554246248347871976052359977691923235702203053028403859154149710724295592067062025095201759631858727663599752836634310801506658537106473285386259222605822205104036802702975047987280794616581004170526819400190957334621759438936702493204226910343698124637201111852610842689102997203112021000635071763745824052038475551972799337976149061078949855442233260040188513036315611448868472815892881632451872650666453848775991625766428721112408420680167635171001029431807155151909616424609070394081292169035174929613640041396704310412536323270309225773279602923765977455370954691157421404242307819923276174019064245124548775168626961053336942162136053946042456541401285330078136334498567364067039773422298119610429255345016014059404795471545345484072717376562623665491666402330060132657440701078368584684523131604677544805004022406399119703622186029202388671507110171694002968687596635000408953162142334252279568340670134701859020283607167621477434934495635958080821304425864694685226……………

The above number is generated to 2000 decimal places. I name this number the

The reason why I call it the

Rv^2 = 13.928..

Rv^3 = 51.9807..

Rv^4 = 193.9948..

Rv^5 = 723.99961..

Rv^6 = 2701.99962..

.

.

Rv^10 = 524173.999998092...

Rv^20 = 274758382273.99999999999636...

Rv^21 = 1025412242451.999999999999024...

Rv^41=281740608900066187095843.999999999999999999999996450...

OK I think I made my point.

Is Rv unique or do other such numbers exist?

Is Rv new or are there existing references to it?

Is Rv a irrational number even though the approximation is rational?

Can I say that Rv raised to infinity is a infinate large integer? [edit] I rephrase after Data's comment"Rv raised to infinity is a integer quantity?"

3.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067030299699450949989524788116555120943736485280932319023055820679748201010846749232650153123432669033228866506722546689218379712270471316603678615880190499865373798593894676503475065760507566183481296061009476021871903250831458295239598329977898245082887144638329173472241639845878553976679580638183536661108431737808943783161020883055249016700235207111442886959909563657970871684980728994932964842830207864086039887386975375823173178313959929830078387028770539133695633121037072640192491067682311992883756411414220167427521023729942708310598984594759876642888977961478379583902288548529035760338528080643819723446610596897228728652641538226646984200211954841552784411812865345070351916500166892944154808460712771439997629268346295774383618951101271486387469765459824517885509753790138806649619119622229571105552429237231921977382625616314688420328537166829386496119170497388363954959381457576718533736331259108996554246248347871976052359977691923235702203053028403859154149710724295592067062025095201759631858727663599752836634310801506658537106473285386259222605822205104036802702975047987280794616581004170526819400190957334621759438936702493204226910343698124637201111852610842689102997203112021000635071763745824052038475551972799337976149061078949855442233260040188513036315611448868472815892881632451872650666453848775991625766428721112408420680167635171001029431807155151909616424609070394081292169035174929613640041396704310412536323270309225773279602923765977455370954691157421404242307819923276174019064245124548775168626961053336942162136053946042456541401285330078136334498567364067039773422298119610429255345016014059404795471545345484072717376562623665491666402330060132657440701078368584684523131604677544805004022406399119703622186029202388671507110171694002968687596635000408953162142334252279568340670134701859020283607167621477434934495635958080821304425864694685226……………

The above number is generated to 2000 decimal places. I name this number the

*Near Integer Ratio*Rv, it is generated by a simple algorithm and is approximated by Rv=P[n]/P[n-1]. The number of iteration steps n gives the relevant number of decimal places or precision. Interesting the integer quantities P[n] and P[n-1] have no common divisors or factors.The reason why I call it the

*near integer ratio*is that Rv exhibits following property that when Rv raised to the power of 2m (m<n) or 2m+1 the result has more than m recurring nines after the decimal point, i.e. Rv^2m is a*near integer quantity*.Rv^2 = 13.928..

Rv^3 = 51.9807..

Rv^4 = 193.9948..

Rv^5 = 723.99961..

Rv^6 = 2701.99962..

.

.

Rv^10 = 524173.999998092...

Rv^20 = 274758382273.99999999999636...

Rv^21 = 1025412242451.999999999999024...

Rv^41=281740608900066187095843.999999999999999999999996450...

OK I think I made my point.

Is Rv unique or do other such numbers exist?

Is Rv new or are there existing references to it?

Is Rv a irrational number even though the approximation is rational?

Can I say that Rv raised to infinity is a infinate large integer? [edit] I rephrase after Data's comment"Rv raised to infinity is a integer quantity?"

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