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The Multiplication Problem for Spheres
Howard Stauffer
. The multiplication problem for spheres is to determine which spheres in Euclidean space Sn-1 -"º En permit a continuous multiplication. This paper presents the topological K-theory proof that it is only possible when n = 1, 2, 4, and 8. These cases correspond to S0 -"º E1, S1 -…
. The multiplication problem for spheres is to determine which spheres in Euclidean space Sn-1 -"º En permit a continuous multiplication. This paper presents the topological K-theory proof that it is only possible when n = 1, 2, 4, and 8. These cases correspond to S0 -"º E1, S1 -"º E2, S3 -"º E4, and S7 -"º E8 where the multiplications are given respectively by the real numbers, complex numbers, quaternions, and Cayley numbers. Ringkasan. Masalah pendarapan bagi bola adalah masalah untuk menentukan bola-bola dalam Ruang Euclid Sn-1 -"º En membenarkan suatu pendarapan yang kontinu. Tulisan ini…
RIngkasan. Dalam tahun 1971 di daerah Cagar Alam Telaga Patengan telah dilakukan penelitian mengenai macam makanan, bentuk morfologi, aktifitas dan keadaan lingkungan bagi Rana chalconota dan R. nicobariensis. Disusun pula "checklist" Amphibia yang terdapat di daerah tersebut Analisa isi lambung memperlihatkan bahwa masing-masing katak menyukai jenis serangga yang menempati habitat sama dengan katak pemangsanya.Abstract. Studies on the feeding habits, morphology, activity and environmental condition at Rana chalconota and R. nicobariensis were carried out in 1971 at Telaga Patengan Nature…