The seasonal cycle in Arctic sea ice extent is asymmetric. Its amplitude has grown in recent decades as the ice has retreated more rapidly in summer than in winter. These seasonal disparities have typically been attributed to different physical factors operating during different seasons. Here we show instead that the seasonal asymmetries in Arctic sea ice extent are a geometric consequence of the distribution of continents. Coastlines block southward ice extension during winter, thereby muting changes in ice extent, but they have relatively little effect at the time of summer minimum extent. We suggest that the latitude of the Arctic sea ice edge, averaged zonally over locations where it is free to migrate, is the most readily interpretable quantity to describe the Northern Hemisphere sea ice cover. We find that the zonal-mean sea ice edge latitude during the 1978–present era of satellite measurements has been following an approximately sinusoidal seasonal cycle that has been migrating northward at an approximately annually constant rate of 8 km/year. These results suggest a change in perspective of the most critical quantities for understanding changes in Arctic sea ice.