Pythagoras – The Father of Numbers Maths in Action 71

By R. N. A. de Silva

3ythagoras was a Greek PathePatiFian anG ShilosoSher who liYeG arounG %C on an islanG FalleG 6aPos in GreeFe

/ater 3ythagoras PoYeG to Croton in 6outhern ,taly where he starteG his sFhool +is followers were known as 3ythagorean sFholars

$s a PathePatiFian he is known as the ¶father of nuPEers· or as the Àrst Sure PathePatiFian +e is Eest known for his 3ythagorean TheoreP on the relation Eetween the siGes of a right triangle, where the area of the square whose siGe is the hySotenuse is equal to the sum of the areas of the squares on the other two siGes

%esiGes 3ythagoras Theorem, there are many other FontriEutions maGe Ey 3ythagoras +e reÁeFteG more on the mystiFal stuGy of mathematiFs rather than its SraFtiFal aSSliFation 3ythagoras starteG the iGea of a numeriFal system, anG therefore the Eeginning of mathematiFs

The EasiF iGea of 3ythagorean 6Fhool was ´$ll is numEerµ They EelieYeG that eaFh numEer has its meaning anG FharaFter 2GG numEers were FonsiGereG as female anG eYen numEers as male

+e Fan also Ee FonsiGereG as the ¶father of harmony· FonsiGering his FontriEutions to the ÀelG of musiF 2ne Gay, he was Sassing Ey a ElaFksmith anG founG the sounG of a hammer to Ee musiFal +e went insiGe anG starteG Eeating hammers of Gifferent si]es on a taEle anG oEserYeG that the tune SlayeG Ey the hammer was GireFtly proportional to the size of the hammer. 3ythagoras anG his followers later founG that a string of a partiFular thiFkness anG length makes a partiFular sounG, whereas a string of half of its length will make the same sounG Eut on a higher note. They useG ratio for oFtaYe, for perfeFt Àfth anG for perfeFt fourth.

,n aGGition to the famous 3ythagoras Theorem, 3ythagoreans also maGe many other FontriEutions in geometry some of whiFh are stateG Eelow.

The sum of the internal angles of a z triangle equals two right angles. The sum of the external angles of a z triangle equals four right angles. The sum of the interior angles of any z polygon is n right angles, where n is the numEer of siGes. The sum of the exterior angles of z a polygon equals four right angles, howeYer many siGes.

The three polygons, the triangle, z hexagon anG square, Fompletely Àll the spaFe arounG a point on a plane. <ou Fan tile an area with these three shapes, without leaving gaps or having overlaps. 3ythagoras is also FreGiteG with the GisFovery of Àve regular soliGs FuEe, triangle, oFtaheGron, GoGeFaheGron anG iFosaheGron.

3roperties of these soliGs were further elaEorateG Ey 3lato anG henFe these are nameG after him as 3latoniF soliGs.

3ythagoreans were the Àrst to iGentify the perfeFt numEers.

3erfeFt numEers are those numEers that are equal to the sum of their proper Givisors. is a perfeFt numEer EeFause

anG is a perfeFt numEer as . /ater (uFliG proveG that ˤ is an even perfeFt

pˤ p numEer whenever ˤ is prime.

p

The Àrst three perfeFt numEers generateG Ey the formula ˤ ,

pˤ p with p as a prime numEer are

)or p ˤ ˷

)or p ˤ ˷

)or p ˤ ˷

Can you ÀnG the next perfeFt numEer"