 sopha sthiraamkam yokka itivali eguva bound mariyu takuva bound ‌ lanu sangrahinchi ,  vatini phormat  { bound taaip } - { bound vaalyuu } loo tirigi ivvande .
 sopha sthiraamkam  (A)  nirdishta viluvalaku  ( takuva haddulu mariyu eguva sarihaddulu )  diguvana ledha anthakante ekuva undakoodadani niroopinche pania jargindi .

 dhiguva 
 spastamaina dhiguva sarihaddu  A \geq \pi/2 \  sumaaru  1.57.  idi unit vyaasaartham yokka sagam - disick ayina sopha nundi osthundi ,  idi moolalo tippavachhu .

 jeanne hamersley ooka telephony handed ‌ sett ‌ nu pooli umdae aakriti aadhaaramga  A \geq \pi/2 + 2/\pi \  sumaaru  2.2074  yokka takuva parimitini pondhaaru , 1  by  4/\ ki iruvaipula vyaasaartham  1  yokka remdu quuarter - disick ‌ lu untai . pi  deerghachaturasram deeni nundi vyaasaartham yokka sagam - disick .

1992 loo ,  rutgers univarsitiiki chendina josep emle .  gerver  18  karv section ‌ l dwara varninchabadina sophanu okkokkati sunnitamaina vishlaeshanhaatmaka rupaanni teesukuntundani vivarinchaadu .  idi sopha sthiraamkam yokka dhiguva sarihaddunu sumaarugaa  2.2195 ki pemchimdi .

 eguva 

 hamersley sopha sthiraamkampai eguva sarihaddunu kudaa kanugonnaadu ,  idi garishtamgaa  2\sqrt{2} \ sumaaru  2.8284  ani chupistundi .

 yov kallas mariyu dawn romic juun  2017 loo kothha unnanatha stayini niroopinchaaru ,  sopha sthiraankaanni  2.37  oddha muginchaaru .
 mruduvaina sthiraamkam krindhi sarihaaddulanu kaligi umtumdi :  eguva bound  - 2.37,  dhiguva bound  - 2.2195.