▁granted ▁a ▁pat ent ▁in ▁Britain ▁for ▁Roman ▁c ement ▁(" A ▁certain ▁C ement ▁or ▁Terr as ▁to ▁be ▁used ▁in ▁Aqu atic ▁and ▁other ▁Build ings ▁and ▁Stu cco ▁Work "). ▁ ▁Ex pl oration ▁ ▁June ▁ 2 1 ▁– ▁M ung o ▁Park ▁becomes ▁the ▁first ▁European ▁to ▁reach ▁the ▁Niger ▁River . ▁ ▁Mathemat ics ▁ ▁This ▁is ▁a ▁product ive ▁year ▁for ▁the ▁German ▁math ematic ian ▁Carl ▁Friedrich ▁G auss ▁( born ▁ 1 7 7 7 ) ▁and ▁his ▁work ▁in ▁number ▁theory : ▁ ▁March ▁ 3 0 ▁– ▁He ▁obtain s ▁conditions ▁for ▁the ▁construct ibility ▁by ▁r uler ▁and ▁comp ass ▁of ▁regular ▁pol yg ons , ▁including ▁the ▁he pt ade c agon . ▁ ▁April ▁ 8 ▁– ▁He ▁becomes ▁the ▁first ▁to ▁prove ▁the ▁quadratic ▁reci pro city ▁law , ▁en abling ▁determ ination ▁of ▁the ▁sol v ability ▁of ▁any ▁quadratic ▁equation ▁in ▁mod ular ▁arithmetic . ▁ ▁May ▁ 3 1 ▁– ▁He ▁puts ▁forward ▁his ▁prime ▁number ▁theorem ▁on ▁the ▁distribution ▁of ▁prime ▁numbers ▁among ▁the ▁integers . ▁ ▁July ▁ 1 0 ▁– ▁He ▁disco vers ▁that ▁every ▁positive ▁integer ▁is ▁represent able ▁as ▁a ▁sum ▁of ▁at ▁most ▁three ▁tri angular ▁numbers , ▁not ing ▁in ▁his ▁di ary ▁" He ure ka ! ▁num   =   Δ   +   Δ   +   Δ ." ▁ ▁October ▁ 1 ▁– ▁He ▁publish es ▁a ▁result ▁on ▁the ▁number ▁of ▁solutions ▁of