Pythagorean hypotenuses as contraharmonic means

$c^{2}\;=\;a^{2}+b^{2}$ $\displaystyle c\;=\;\frac{u^{2}+v^{2}}{u+v}$ N.B.
$5^{2}=3^{2}+4^{2}$ $5=(2^{2}+6^{2})/(2+6)$ 3
$10^{2}=6^{2}+8^{2}$ $10=(6^{2}+12^{2})/(6+12)$
$13^{2}=5^{2}+12^{2}$ $13=(3^{2}+15^{2})/(3+15)$ 5
$15^{2}=9^{2}+12^{2}$ $15=(9^{2}+18^{2})/(9+18)$
$17^{2}=8^{2}+15^{2}$ $17=(5^{2}+20^{2})/(5+20)$ 5
$20^{2}=12^{2}+16^{2}$ $20=(8^{2}+24^{2})/(8+24)$
$25^{2}=7^{2}+24^{2}$ $25=(4^{2}+28^{2})/(4+28)$ 7
$26^{2}=10^{2}+24^{2}$ $26=(6^{2}+30^{2})/(6+30)$
$29^{2}=20^{2}+21^{2}$ $29=(14^{2}+35^{2})/(14+35)$ 7
$30^{2}=18^{2}+24^{2}$ $30=(12^{2}+36^{2})/(12+36)$
$34^{2}=16^{2}+30^{2}$ $34=(10^{2}+40^{2})/(10+40)$ 5
$35^{2}=21^{2}+28^{2}$ $35=(14^{2}+42^{2})/(14+42)$
$37^{2}=12^{2}+35^{2}$ $37=(30^{2}+42^{2})/(30+42)$ 7
$39^{2}=15^{2}+36^{2}$ $39=(9^{2}+45^{2})/(9+45)$
$40^{2}=24^{2}+32^{2}$ $40=(16^{2}+48^{2})/(16+48)$
$41^{2}=9^{2}+40^{2}$ $41=(36^{2}+45^{2})/(36+45)$ 3
$50^{2}=14^{2}+48^{2}$ $50=(42^{2}+56^{2})/(42+56)$ 7
$51^{2}=24^{2}+45^{2}$ $51=(15^{2}+60^{2})/(15+60)$
$52^{2}=20^{2}+48^{2}$ $52=(12^{2}+60^{2})/(12+60)$ 3
$53^{2}=28^{2}+45^{2}$ $53=(18^{2}+63^{2})/(18+63)$ 7
$55^{2}=33^{2}+44^{2}$ $55=(22^{2}+66^{2})/(22+66)$
$58^{2}=40^{2}+42^{2}$ $58=(30^{2}+70^{2})/(30+70)$ 7
$60^{2}=36^{2}+48^{2}$ $60=(24^{2}+72^{2})/(24+72)$
$61^{2}=11^{2}+60^{2}$ $61=(6^{2}+66^{2})/(6+66)$ 11
$61^{2}=11^{2}+60^{2}$ $61=(55^{2}+66^{2})/(55+66)$ 11

$65^{2}=39^{2}+52^{2}$
$65=(26^{2}+78^{2})/(26+78)$
$68^{2}=32^{2}+60^{2}$ $68=(20^{2}+80^{2})/(20+80)$
$70^{2}=42^{2}+56^{2}$ $70=(28^{2}+84^{2})/(28+84)$
$73^{2}=48^{2}+55^{2}$ $73=(40^{2}+88^{2})/(40+88)$ 11
$74^{2}=24^{2}+70^{2}$ $74=(14^{2}+84^{2})/(14+84)$ 7
$75^{2}=21^{2}+72^{2}$ $75=(12^{2}+84^{2})/(12+84)$ 7
$78^{2}=30^{2}+72^{2}$ $78=(18^{2}+90^{2})/(18+90)$
$80^{2}=48^{2}+64^{2}$ $80=(32^{2}+96^{2})/(32+96)$
$82^{2}=18^{2}+80^{2}$ $82=(10^{2}+90^{2})/(10+90)$ 3
$85^{2}=40^{2}+75^{2}$ $85=(25^{2}+100^{2})/(25+100)$
$87^{2}=60^{2}+63^{2}$ $87=(42^{2}+105^{2})/(42+105)$ 7
$89^{2}=39^{2}+80^{2}$ $89=(24^{2}+104^{2})/(24+104)$ 13
$90^{2}=54^{2}+72^{2}$ $90=(36^{2}+108^{2})/(36+108)$
$91^{2}=35^{2}+84^{2}$ $91=(21^{2}+105^{2})/(21+105)$
$95^{2}=57^{2}+76^{2}$ $95=(38^{2}+114^{2})/(38+114)$ 19
$97^{2}=72^{2}+65^{2}$ $97=(45^{2}+117^{2})/(45+117)$ 13
$100^{2}=60^{2}+80^{2}$ $100=(40^{2}+120^{2})/(40+120)$

 Title Pythagorean hypotenuses as contraharmonic means Canonical name PythagoreanHypotenusesAsContraharmonicMeans Date of creation 2013-11-20 20:23:01 Last modified on 2013-11-20 20:23:01 Owner pahio (2872) Last modified by pahio (2872) Numerical id 10 Author pahio (2872) Entry type Data Structure Classification msc 11Z05 Classification msc 11D45 Classification msc 11D09 Classification msc 11A05 Related topic PythagoreanTriple Related topic ContraharmonicMean Related topic FirstPrimitivePythagoreanTriplets Related topic ContraharmonicProportion