« 【数学】 Ratio of Triangle Area りんぺん比 解説用の図 | トップページ | Counting »

【数学】 Ceva's Theorem メネラウスの定理 チェバの定理 解説用の図

https://remedics.air-nifty.com/photos/hawaii/ceva35.png

https://remedics.air-nifty.com/photos/hawaii/ceva29.png

Let's try an example.

What is the ratio of  ?/? of the following triangle?

https://remedics.air-nifty.com/photos/hawaii/ceva2.png

This is how to figure it out...

https://remedics.air-nifty.com/photos/hawaii/ceva30.png

https://remedics.air-nifty.com/photos/hawaii/ceva31.png

https://remedics.air-nifty.com/photos/hawaii/ceva32.png

Let's go one step further.

 

Adjust the ratio so as for A and D to be the same number.

https://remedics.air-nifty.com/photos/hawaii/ceva33.png

Then, it always happens to be the fact that A = D, B = E, C = F.


Now you get the 3 numbers!


https://remedics.air-nifty.com/photos/hawaii/ceva34.png

https://remedics.air-nifty.com/photos/hawaii/ceva1.png


This is how you use these 3 numbers.

https://remedics.air-nifty.com/photos/hawaii/ceva7.png

https://remedics.air-nifty.com/photos/hawaii/ceva8.png

https://remedics.air-nifty.com/photos/hawaii/ceva9.png

For example, if the there numbers are 6, 4, and 3, …

https://remedics.air-nifty.com/photos/hawaii/ceva10.png

https://remedics.air-nifty.com/photos/hawaii/ceva11.png

https://remedics.air-nifty.com/photos/hawaii/ceva12.png

You can also figure out the ratio of the area of the 3 small triangles inside.

https://remedics.air-nifty.com/photos/hawaii/ceva13.png

https://remedics.air-nifty.com/photos/hawaii/ceva14.png

https://remedics.air-nifty.com/photos/hawaii/ceva15.png




Let's try a sample question.

What is the ratio?

https://remedics.air-nifty.com/photos/hawaii/ceva16_2.png

Could you figure it out?

 

Solution

https://remedics.air-nifty.com/photos/hawaii/ceva17.png

https://remedics.air-nifty.com/photos/hawaii/ceva18.png

https://remedics.air-nifty.com/photos/hawaii/ceva19.png

https://remedics.air-nifty.com/photos/hawaii/ceva36.png

https://remedics.air-nifty.com/photos/hawaii/ceva37.png

Finally, you get the ratio on the all sides.

https://remedics.air-nifty.com/photos/hawaii/ceva38.png

Do some adjustment, and get the magical 3 numbers!

https://remedics.air-nifty.com/photos/hawaii/ceva39.png

In this case, those numbers are 2, 3, 4.

With those 3 numbers, you can figure out all of the following ratios!!!

https://remedics.air-nifty.com/photos/hawaii/ceva26.png

« 【数学】 Ratio of Triangle Area りんぺん比 解説用の図 | トップページ | Counting »

コメント

コメントを書く

コメントは記事投稿者が公開するまで表示されません。

(ウェブ上には掲載しません)

« 【数学】 Ratio of Triangle Area りんぺん比 解説用の図 | トップページ | Counting »