1. Fill a small saucepan with water. Bring to a boil and add salt. When water returns to a boil, reduce heat to a simmer. Add beets and cook until tender, about 20 minutes. Drain and let cool. Cut beets into 4-by-2-inch slices; place in a large bowl.

2. Using a zester or vegetable peeler, zest the rind of one of the oranges. Finely chop and add to another large bowl along with the lime juice, orange juice, 1/2 teaspoon salt, sugar, and oil. Mix well and pour over beets; let stand 1 hour.

3. Remove peel and pith from the oranges using a sharp paring knife. Carefully cut between membranes to remove segments; set aside.

4. Add jicama and orange segments to the beet mixture and season with salt. Place arugula on a serving platter and place beet mixture on top. Sprinkle with peanuts and garnish with sugar can cane.