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Dhacorrea

aka Daniel Corrêa

  • I live in Brazil
  • I was born on November 17
  • My occupation is I'm Ph.D/M.Sc. in Biochemistry, graduated in Biomedicine, and I love math and many curiosities related to this amazing field.
  • I am Male
  • Dhacorrea

    Steinhaus-Moser Notation is a well know notation created by Hugo Steinhaus, and extended by Leo Moser.

    My intention in this post is to show the resolution of some 2's inside polygons of Steinhaus-Moser notation. It´s well know that the first polygon is the triangle, and any number \(n\) inside a triangle is converted to the \(n\) power of \(n\) or \(n^{n}\).

    Here we represent a value \(n\) inside a triangle as \(n[3]_{1}\), according the general notation proposed by Susan Stepney. The notation extends to:

    • ​\(n\) inside a square or \(n[4]_{1}\) = \(n\) inside \(n\) triangles = \(n[3]_{n}\);
    • \(n\) inside a pentagon or \(n[5]_{1}\) = \(n\) inside \(n\) squares = \(n[4]_{n}\);
    • \(n\) inside a hexagon or \(n[6]_{1}\) = \(n\) inside \(n\) pentagons = \…
    Read more >
  • Dhacorrea

    Sumselfgogopyr

    February 25, 2016 by Dhacorrea

    Sumselfgogopyr is defined as the summation of the n-th n-gonal pyramidal numbers with n from 3 to gogopyr, the term was coined by Daniel Corrêa.

    Sumselfgogopyr is computed as described below:

    \(Sumselfgogopyr  = \sum^{gogopyr}_{n=3} \frac{3 \cdot n^{2} + n^{3} \cdot (n-2) - n \cdot (n-5)}{6}\)

    Sumselfgogopyr has 1995 digits, and according to the calculations using BCalc to convert gogopyr to power of 10 notation, and using WolframAlphato perform the calculation with the maximum input length, the approximated form of sumselfgogopyr is:

    \(Sumselfgogopyr \approx 4.28669410150... \times 10^{1994}\)

    Read more >
  • Dhacorrea

    Selfgogopyr

    February 24, 2016 by Dhacorrea

    Selfgogopyr is defined as the gogopyrth gogopyrgonal pyramidal number. The term was coined by Daniel Corrêa.

    Selfgogopyr is computed using the general formula for an r-gonal pyramidal number described below:

    \([3.n^{2} + n^{3}.(r-2) - n.(r-5)]/6\)

    where \(r = n = gogopyr\).

    Selfgogopyr has 1597 digits, and according to the calculations performed using BCalc configured to show 2011 digits, the full decimal form is:

    Read more >
  • Dhacorrea

    Sumgogopyr

    February 24, 2016 by Dhacorrea

    Sumgogopyr is defined as the summation of the n-th n-gonal pyramidal numbers with n from 3 to googol, the term was coined by Daniel Corrêa.

    Sumgogopyr is computed as described below:

    \(Sumgogopyr = \sum^{googol}_{n=3} \frac{3 \cdot n^{2} + n^{3} \cdot (n-2) - n \cdot (n-5)}{6}\)

    In its decimal form, sumgogopyr has 499 digits as described: 3 as the first 299 digits followed by the digit 8 followed by a sequence of 99 3's followed by the digit 7 followed by a sequence of 98 9's, and 6 as the last digit.

    The full decimal form of sumgogopyr is expressed below:

    Read more >
  • Dhacorrea

    Gogopyr

    February 23, 2016 by Dhacorrea

    Gogopyr is defined as the googolth googolgonal pyramidal number. The term was coined by Daniel Corrêa.

    Gogopyr is computed using the general formula for an r-gonal pyramidal number described below:

    \([3.n^{2} + n^{3}.(r-2) - n.(r-5)]/6\)

    where \(r = n = 10^{100}\).

    In its full decimal form, gogopyr has 400 digits as described: 1 as the first digit followed by 99 6's in sequence followed by 100 3's in sequence followed by 99 6's in sequence followed by the digits 7 and 5, and finally followed by 99 0's in sequence.

    The full decimal form of gogopyr is expressed below:

    Read more >

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