2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187672The new 182 gold supernova Ia data, the baryon acoustic oscillation measurement and the shift parameter determined from the Sloan Digital Sky Survey and the three-year Wilkinson Microwave Anisotropy Probe data are combined to reconstruct the dark energy equation of state parameter $w(z)$ and the deceleration parameter $q(z)$. We find that the strongest evidence of acceleration happens around the redshift $z\sim 0.2$ and the stringent constraints on $w(z)$ lie in the redshift range $z\sim 0.2-0.5$. At the sweet spot, $-1.2<w(z)<-0.6$ for the dark energy parametrization $w(z)=w_0+w_a z/(1+z)^2$ at the $3σ$ confidence level. The transition redshift $z_t$ when the Universe underwent the transition from deceleration to acceleration is derived to be $z_t=0.36^{+0.23}_{-0.08}$. The combined data is also applied to find out the geometry of the Universe, and we find that at the $3σ$ confidence level, $|Ω_k|\alt 0.05$ for the simple one parameter dark energy model, and $-0.064<Ω_k<0.028$ for the $Λ$CDM model.9 figures, added four contour plots and some discussions on the sweet spot, main conclusion unchanged; v3: references added, PRD in pressAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext