Tag: digit

透過手機螢幕上的餘熱猜測 PIN 碼

利用手機螢幕上的餘熱分析可能的 PIN 碼：「Heat traces left by fingers can reveal your smartphone PIN」，在輸入完 PIN 碼的 30 秒內的準確度都還是很高 (80%)：

The report further revealed that if the thermal image is collected within 15 seconds of a PIN being entered, the technique is accurate almost 90% of the time. At 30 seconds, this accuracy decreased slightly to 80%. At 45 seconds or more, the accuracy dropped to 35% and below.

計算圓周率 Pi 的公式...

在 Twitter 上看到這個：

利用這個公式 (Bailey–Borwein–Plouffe formula)，可以直接對二進位 (四進位、八進位、十六進位、...) 直接計算出某個位數的值...

NASA 的 JPL 回答「你們用的圓周率是 3.14 嗎？」的問題

NASA 的 JPL 回答了他們所使用的圓周率：「How Many Decimals of Pi Do We Really Need?」。

答案是小數下十五位：

For JPL's highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793.

先拿目前離地球最遠的人造物 Voyager 1 來舉例，約 201 億公里 (125 億英里) 的距離，使用這個小數下 15 位的圓周率，與實際的圓周率算出來的誤差只有 3.81 公分 (1.5 英寸)：

The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away.

It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.

另外還舉了地球與整個宇宙的數字來計算，需要的精確度沒有想像中那麼大 XD