Khipha umkhawulo ongenhla nomkhawulo ophansi wakamuva wesofa njalo bese uwabuyisela ngefomethi ethi {Bound Type} - {Bound Value}.
Context:Kuye kwenziwa umsebenzi wokufakazela ukuthi i-constant sofa (A) ayikwazi ukuba ngaphansi noma ngaphezulu kwamanani athile (imingcele engezansi nemingcele ephezulu).  Ngezansi Umkhawulo ophansi obonakalayo ngu-A \geq \pi/2 \approx 1.57. Lokhu kuvela kusofa eliyingxenye yediski enobubanzi obuyiyunithi, elingazungeza ekhoneni.  UJohn Hammersley wakhipha umkhawulo ophansi ka-A \geq \pi/2 + 2/\pi \approx 2.2074 ngokusekelwe ekwakhekeni okufana nesethi yocingo, equkethe ama-quarter-discs amabili enobubanzi obuyi-1 ezinhlangothini zombili ze-rectangle engu-1 ngo-4/\pi lapho uhhafu-we-disc enobubanzi.  Ngo-1992, uJoseph L. Gerver waseRutgers University wachaza usofa ochazwe yizigaba ezijikayo ezingu-18 ngasinye sithatha isimo sokuhlaziya esibushelelezi. Lokhu kwaqhubeka kwandisa umkhawulo ophansi wesofa njalo cishe ku-2.2195.  Okungaphezulu  UHammersley futhi wathola umkhawulo ongaphezulu ku-constant yesofa, okukhombisa ukuthi okungenani u-2\sqrt{2} \approx 2.8284.  U-Yoav Kallus noDan Romik baqinisekisa umkhawulo omusha ophakeme ngoJuni 2017, bavala umbhede wesofa ohlala njalo ngo-2.37.
I-constant ethambile inemikhawulo elandelayo: Umkhawulo Ophezulu - 2.37, Umkhawulo Ophansi - 2.2195.