⍝ Hypersphere surface area: ⎕pp←5 ⍝ 1-sphere is a circle: 1 ksphere 10 ⍝ circumference of circle, radius 10. 62.832 vs ← {(⍺⍺ ⍵)≡⍵⍵ ⍵} ⍝ compare methods. 1∘ksphere vs (2∘×∘○) ⍳10 ⍝ 1-sphere: compare with 2 × Pi × r. 1 ⍝ 2-sphere is a reqular sphere in 3-space: 2 ksphere 10 ⍝ surface area of sphere, radius 10. 1256.6 2∘ksphere vs (4∘×∘○∘(*∘2)) ⍳10 ⍝ 2-sphere: compare with 4 × Pi × r-squared. 1 (0 to 10) ksphere 1 ⍝ surface of unit ⍺-spheres. 2 6.2832 12.566 19.739 26.319 31.006 33.073 32.47 29.687 25.502 20.725 6.2569 ksphere 1 ⍝ max area of unit ⍺-sphere. 33.161 kvol ← {⍵×((⍺-1) ksphere ⍵)÷⍺} ⍝ volume of ⍺-ball of radius ⍵. (0 to 10) kvol 1 ⍝ volumes of unit ⍺-balls. 1 2 3.1416 4.1888 4.9348 5.2638 5.1677 4.7248 4.0587 3.2985 2.5502 Back to: code Back to: Workspaces