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本期問題的解答請在1956年9月20日以前寄到北京德胜門外北京师范大学数学系轉“数学通报数学問题解答”欄工作組收。問題的答案及正确解答者的姓名將在本刊1956年11月号的本攔內公佈,本欄欢迎讀者提出适合大家解答的問題,最好附有答案。非属本欄的信件,請直接寄給“数学通报編輯部”,幸勿投寄本欄,以免延誤或遺失。 1956年8月号問题 253.設△ABC各边BC=a,CA=b,AB=c,∠CAB=α,∠ABC=β,∠BCA=γ。求证:(π/3)≤(aα+bβ+cγ)/(a+b+c)<π/2。 254.四面体的各面若为等积的三角形,則各面亦必为全等的三角形。試証之。
Answers to this issue should be sent to the Working Group of Mathematics Department of Beijing Normal University outside Beijing Deshengmen before September 20, 1956. The answer to the question and the name of the correct answerer will be published in this column in the November 1956 issue of this issue. This column welcomes readers to ask questions that are suitable for everyone’s answers, preferably with answers. Letters not belonging to this column should be sent directly to the “Editor’s Office of the Mathematics Bulletin.” Fortunately, do not post this column to avoid delay or loss. August 1956 issue 253. Let ABC sides BC=a, CA=b, AB=c, ∠CAB=α, ∠ABC=β, ∠BCA=γ. Proof: (π/3) ≤ (aα+bβ+cγ)/(a+b+c)<π/2. 254. If all sides of the tetrahedron are equal triangles, then all sides must also be equal triangles. Testimony.