The catenoid arises from rotating the catenary curve about a horizontal line. Scherk's result was certainly seen as a major breakthrough and brought him considerable fame; two surfaces, Scherk's First Surface and Scherk's Second Surface, as they are named today, are studied in the paper. Scherk's doubly periodic surface is the first example of a complete, embedded, doubly periodic minimal surface.
Ang catenoid arises mula sa umiikot na ang katenarya curve tungkol sa isang pahalang na linya. Scherk ang resulta ay tiyak na makikita bilang isang pangunahing pambihirang tagumpay at nagdala sa kanya malaki laurel; dalawang ibabaw, Scherk's Unang Surface at Scherk ng Ikalawang Surface, bilang sila ay mga pangalan na ngayon, ang mga aral sa papel. Scherk's doble panaka-ibabaw ay ang unang halimbawa ng isang kumpleto, embed, doble panaka-minimal ibabaw.