random math facts

[matt000r000]

here are some random facts:

arithmatic was created first, but it is founded on geometry.

the word "calculus" means "calculation" but literaly means "counting stone" in latin.

geometry is the study of land, not shapes. "geometry" literaly means "land measurement" in greek. thats why "geography" and "geometry" sound similar.

mathematics is the study of paterns, not numbers. arithmatic is the study of numbers, and technicly its quantities.

post any other random math facts here.

 

[mmm4444bot]

... arithmatic (sic) ... is founded on geometry ...

... geometry is the study of land ...

Please cite your source for the "fact" that arithmetic is founded on the study of land.

 

[soroban]

. . .
. . More Random Facts



. . \(\displaystyle \begin{array}{ccc}1,\!001 &=& 7\cdot11\cdot13 \\ 10,\!001 &=& 73\cdot137 \\ 1,\!000,001 &=& 101\cdot 9901 \\ 10,\!000,\!001 &=& 11\cdot909091 \end{array}\)



. . \(\displaystyle \begin{array}{ccc}111 &=& 3\cdot37 \\ 1,\!111 &=& 11\cdot101 \\ 11,\!111 &=& 41\cdot271 \\ 111,\!111 &=& 3\cdot7\cdot11\cdot13\cdot37 \\ 1,\!111,\!111 &=& 239\cdot 4649 \\ 11,\!111,\!111 &=& 11\cdot73\cdot101\cdot137 \\ 111,\!111,\!111 &=& 9\cdot37\cdot333667 \end{array}\)



. . \(\displaystyle \begin{array}{ccc}\dfrac{37^3+13^3}{37^3+24^3} \;=\;\dfrac{37+13}{37+24} \\ \\[-2mm] \dfrac{3^4 + 25^4+38^4}{7^4+20^4+39^4} \;=\;\dfrac{3+25+38}{7+20+39} \end{array}\)



. . \(\displaystyle \begin{array}{ccc}168 \times 861 &=& 294 \times 492 \\ 276 \times 672 &=& 384 \times 483 \\ 1476 \times 6741 &=&2583 \times 3852\\ 2556 \times 6552 &=& 3744 \times 4473 \end{array}\)



A classic "oldie"

\(\displaystyle \text{Solve: }\:a^b \:=\:b^a\,\text{ in rational numbers.}\)

\(\displaystyle \text{Most people know that: }\:2^4 \:=\:4^2\)
\(\displaystyle \text{But very few of us know that: }\:\left(\frac{27}{8}\right)^{\frac{9}{4}} \;=\;\left(\frac{9}{4}\right)^{\frac{27}{8}}\)

 

[daon]

Soroban reminded me: powers of 11 up to 4 represent those rows of Pascal's Triangle.

\(\displaystyle \begin{array}{ccc} 11^0 = 1 \\ 11^1 = 11 \\ 11^2 = 121 \\ 11^3 = 1331 \\ 11^4 = 14641 \end{array}\)

 

[matt000r000]

Re:

... arithmatic (sic) ... is founded on geometry ...

... geometry is the study of land ...

Please cite your source for the "fact" that arithmetic is founded on the study of land.

it is from God Created the Integers by Stephen Hawking, the subject of the first half of the first chapter. the story basicly goes like this:

arithmatic has been formed. geometry has been formaly formed. then the pathagoreans, a sort of math cult, decided that all of the universe was based on numbers. so, to prove this, they had to set everything in geometry to numbers. to do that, they had to prove that anything you could do in geometry, you could also do in arithmatic. they did fairly well, untill their own creation bit them in the back: the pathagorean theorem. the problem was that they couldn't quantitize the length of the hypotenuse of a right triangle with sides of length 1. now, today we now this length as the square root of 2, an irrational number. but they didn't yet know there was such a thing as an irrational number. so, one of them set out to prove it was a measurable number, even if it was too small for them to measure. and so, the proof of irrational numbers was born, slapping the pathagoreans in the face. geometry could do something arithmatic could not: it could handle irrational numbers. but that means you can't do anything you can do in geometry with arithmatic. so arithmatic could not be the foundation of geometry. but it was fairly easy to flip it around, and say arithmatic is based on geometry, for anything you could do in arithmatic, you could do with geometry. and thus, there we have it! arithmatic is based on geometry!

P.S.
to clairify things, square roots are not considered arithmatic, but algebra. the reason being that algebra can accept as an answer a multiple-number answer, but aritmatic can only have a single number. for example, you can't have 1/2 as an answer in arithmatic, but it is acceptable in algebra! in arithmatic, it would have to be .5. so, you would have to be able to write the square root of 2 with out a square root sign, but since it is infinantly long, it can't be written!