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蘇聯吉西遼夫原著,前東北教育部編譯的高中平面幾何第五章末附有已知底b和高h的弓形面積近似值公式:(1)S=2/3bh和(2)S=2/3bh+h~3/2b。課文中聲明“在這裏不加證明”,劉薰宇先生依據克氏原書修訂的高中平面幾何也照樣采入,在一般學生的心理中總有得不到理論上的解決不能饜足之意,這個問題曾經傅種孫先生依據正切函數的無限展開加以論證(見數學通報1955年6月號),可是,因為屬於高等數學的範圍,不能向小學生介紹,筆者為了滿足學生的求知欲,採取初等數學的極限原理來證明第一公式,至於第二公式,因含有h~3/2b一項,那就非要根據傳種孫先生的證法不可了。
In the original version of the Soviet high school plane geometry compiled by the former Soviet Union’s Jixi Liaofu, the arched area approximation formula for bottom b and height h is known at the end of chapter 5 of the high school plane geometry compiled by the former Northeastern Ministry of Education: (1) S=2/3bh and (2)S=2 /3bh+h~3/2b. The text stated in the text “No proof here”. The high school plane geometry revised by Mr. Liu Xunyu according to the original Krefeld book is still taken in. In the general student’s psychology, there is always no theoretical solution to the problem. This problem was once Mr. Fu Chongsun demonstrated based on the infinite expansion of the tangent function (see the June 1955 in the Mathematics Bulletin). However, because it belongs to the scope of higher mathematics, it cannot be introduced to elementary school students. The author has adopted the limits of elementary mathematics in order to satisfy students’ curiosity. The principle is to prove the first formula. As for the second formula, because it contains h~3/2b, it must be based on Mr. Sun’s proof.