一日受教 终身不忘的西方教育——学数学也是学英语

许多人都知道，即使托福满分，即使数学满分，不见得能听得懂西方老师的数学课，但的学生显然无惧于此，听听他们的数学课，看看下面学生完成的作业，你立刻明白了：GAC的学生为何英文提高如此之快，为什么他们出去什么课程都敢选，为什么他们个个在国外都那么优秀？

以下是GAC学生提交的数学作业：

Introduction:

The purpose of this project is to showcertain characteristics of triangles. I will demonstrate these characteristicsby performing certain measurements and calculations on two triangles. I willmainly calculate the sides, angles, and areas given certain measurements foreach triangle, by making use of certain laws, known as the Law of Sines, theLaw of Cosines, and some formulas for the area of triangles.

I also used a spreadsheet called “Sine,cosine and area rules” to examine whether my calculations right or not.

Analysis of An Obtuse Triangle:

This picture shows an obtuse triangle, forwhich the following information is assumed known. The longest side BC equals to4.14 meters and the other side AC equals to 3 meters. The angle between them ∠C equals to 33 degrees.

Obtuse Angle:

First, we can calculate the obtuse angle asfollows. I use the Cosine law: a2=b2+c2-2bc*cosAto calculate side AB initially. I put BC and AC’s length and ∠C degree into a2=b2+c2-2bc*cosA, AB2=4.142+32-2*4.14*3*cos33°. I can get AB is 2.30meters.

Then, to compute the obtuse angle, I usesine law which is  to calculate the angle A’sdegree. , I can get angle A equals to 101.38 *** measure result is 105 degrees.

Area:

I use area formula which is . A=*4.14*3*sin33°=3.38. After that I use the longest side 4.14 meters andperpendicular height of the triangle 1.64 meters to compute the area of thetriangle: A=1/2*1.64*4.14=3.39. We can see that there aren’t big differencesbetween the results of calculation and measurement.

Analysis of An Acute Triangle

This triangle I drew is an acute triangle, withthe following measured values. AB is 2.28 meters, BC is 3.58 meters, AC is 3.53meters. I can use Cosine Law to compute the three angles. =0.30. Then angle A equals to 72.49 degrees. The measurement resultI got is 71 degrees. Then I use the Cosine Law again to calculate the degree ofangle B: =0.34. Angle B equals to 70.11 degrees which is close to my measurementresult: 68°. =0.80. ∠C=37.40°. It is not close to the measurement result: 41°. I use A= *a*h to calculate the area of acute triangle: A=1/2*2.32*3.58=4.16 m2.

Reconciliation with Spreadsheet:

I used the spreadsheet “Sine, cosine andarea rules” to check my answers. For the obtuse triangle, the obtuse angle Icalculated is 101.38°, the result on the spreadsheet(SAS) is 101.83 degreestoo. As for the other side, the results are the same too: 2.30 meters. Then Iuse the area law to check the obtuse triangle area. My calculation result is3.38 m2. And the spreadsheet says the area is 3.38 m2. For my acute triangle, Iuse SSS to check my answers. The results I get are same to the spreadsheet’s:70.11°, 72.49°and 37.40°. Also the area of the acute triangle is 4.16 m2.

Conclusion:

After the measurement and calculation I performed,I found that there were some errors between them. Because I drew triangles bychalks and used a paper protractor to measure degrees, there must be someerrors. But the areas I calculated are similar.