sasusuan ni pitaguras

madjaludjalu manu pazangal a pinasusuan mavan aicu sasusuan ni pitaguras(畢氏定理) (Pythagorean theorem) a sikinemeneman tua vavuduan/tatideqan nua mareka vecik. makaya sinivecik sa papukeljang a a katua b tua drusa a gidigidian nua ta tjelu a putung, sa tja sinivecik c taza calisilisian. a tja kineljang aicu a sasusuan ni pitaguras mavan a sisupusupu sa paseljang matu:^[1]

${\displaystyle a^{2}+b^{2}=c^{2}.}$

aicu a sususuan a pinapungadan ti piaguras a nasemupu a segeris a kinasicuayan. pasusangas a 1,000 a cavilj tazua, izua za sisupusupu a kineljangan nua caucau i kacauan. ljakua aicu a tja sinipapukeljang a ngadan taicu a sasusuan ni pitaguras tucu.

nu namapacunan a sinivecikan a C a tja sipakeljang tua cacalisian nua ta tjelu a putung, sa pakatua zuma a gidigidian nua za tjelu a putung, izua za sinivecikan a A katua B a sipakeljang, mavan aicu a tja sinipakeljangan a sinisupuan nua sasusuan ni pitaguras:

${\displaystyle a^{2}+b^{2}=c^{2}.}$

nu namasan aicu a tja kineljangan a laladruqan nua A katua B, manu aicu a tja sisupusupu:

${\displaystyle c={\sqrt {a^{2}+b^{2}}}.}$

nu nakemeljang itjen ta laladruqan nua C a cacalisian katua tailj a gidigidian (A ka na ika B), manu aicu a tja sisupusupu tua laladruqan nua zumanga a gidigidian:

${\displaystyle a={\sqrt {c^{2}-b^{2}}}}$

ka na ika mavan aicu a maumalj a sinisupuan:

${\displaystyle b={\sqrt {c^{2}-a^{2}}}.}$

saka, aicu a tja kineljang tu nu kemeljang itjen ta laladruqan nua matjadrusa a gidigidian nua ta tjelu a putung, maqatitjen a semupu sa kemeljang tua laladruqan nua sikamasantjelulj a gidigidian.

a tja sipakasalusalu a masan sepatj a tjelu a putung a pinapeseljang. sa paseljang itjen tua aicu a tjelu a putung itua ta sepatj a putung matu tja mapacuanan taicu a vecik i pasanavalj. a tja sipatjavatan aicu C a tja sipakeljang tua gidigidian nua za sepatj a putung.^[2] nu pasuvililj, izua tjaqaca a sepatj a putung tuki tja kineljang aicu a a + b aza gidigidian, saka sikeljangan tua tatideqan naza sepatj a putung aza sisupuan a (a + b)². penaqulid a patjeseljaseljang a tja mapacunan a laludraqan a cacalisian nua matjasepatj a tjelu a putung a katagiljan tua laladruqan a gidigidian nua sepatj a putung nu tjaivililj. a tja sipatjavatjavat mavan cu a C tua za laludraqan.

${\displaystyle (b+a)^{2}=c^{2}+4{\frac {ab}{2}}=c^{2}+2ab,}$

a pasuvililj avan cu a masan italj a sisupuspu:

${\displaystyle c^{2}=(b+a)^{2}-2ab=b^{2}+2ab+a^{2}-2ab=a^{2}+b^{2}.}$

inka maljian mavan cu a masan italj a sipakasalusalu aza pinaseljangan a masan sepatj a tjelu a putung a pasanavalj (right triangle). a tja sipatjavat a a, b katua c taza gidigidian. pinitaladj aza sepatj a tjelu a putung tua ta sepatj a putung. a tja sipatjavat tua laladruqan a gidigidian nua za sepatj a putung a c.^[3] ika maljian a tatideqan nua za tjelu a putung tua tatideqan a ${\displaystyle {\tfrac {1}{2}}ab}$. saka tja sinipapukeljang a b − a tua gidigidian nua masan italj a kedrian a sepatj a putung; a tja kineljang a (b − a)² tua tatideqan nua za sepatj a putung. a tjaivililj a tja sipapukeljang tua tatideqan nua tjaqaca a sepatj a putung aicu a sisupusupu sa paseljang matu:

${\displaystyle (b-a)^{2}+4{\frac {ab}{2}}=(b-a)^{2}+2ab=b^{2}-2ab+a^{2}+2ab=a^{2}+b^{2}.}$

manu tja kineljang taicu a c a laladruqan a gidigidian nua sepatj a putung; aza c² a tja sipapukeljang tua tatideqan nua za sepatj a putung. saka, mavan cu a tja sisupusupu sa paseljang:

${\displaystyle c^{2}=a^{2}+b^{2}.}$

1. ↑ Judith D. Sally; Paul Sally (2007). "Chapter 3: Pythagorean triples". Roots to research: a vertical development of mathematical problems. American Mathematical Society Bookstore. p. 63. ISBN 978-0-8218-4403-8.
2. ↑ Alexander Bogomolny. "Cut-the-knot.org: Pythagorean theorem and its many proofs, Proof #4". Cut the Knot. Retrieved 4 November 2010.
3. ↑ Alexander Bogomolny. "Cut-the-knot.org: Pythagorean theorem and its many proofs, Proof #3". Cut the Knot. Retrieved 4 November 2010.