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# Dhacorrea

## aka Daniel CorrÃªa

• 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
• ## Steinhaus-Moser: some 2's in step-by-step.

February 3, 2017 by 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. ItÂ´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:

• â€‹$$n$$ 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 = \â€¦
• ## 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 CorrÃªa.

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:

$$Sumselfgogopyr \approx 4.28669410150... \times 10^{1994}$$

• ## Selfgogopyr

February 24, 2016 by Dhacorrea

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

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:

• ## 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 CorrÃªa.

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:

• ## Gogopyr

February 23, 2016 by Dhacorrea

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

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: