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From the lesson and booklet:
The number 142857 is a magical one, the best-known cyclic number in base 10. When you write the fraction 1⁄7 in decimal notation, you get
1⁄7 = 0.142857 142857 142857 ….
1 × 142857 = 142857
2 × 142857 = 285714
3 × 142857 = 428571
4 × 142857 = 571428
5 × 142857 = 714285
6 × 142857 = 857142,
And if you multiply this magical number by 7, then you get
7 × 142857 = 999999.
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From Wiki:
1/7 = 0.142857
2/7 = 0.285714
3/7 = 0.428571
4/7 = 0.571428
5/7 = 0.714285
6/7 = 0.857142
7/7 = 0.999999 = 1
8/7 = 1.142857
9/7 = 1.285714
And
1428572 = 142857 × 142857 = 20408 122449
20408 + 122449 = 142857
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Add a CommentAs advertised, no skills beyond basic algebra to understand how the amazing tricks work. Disc A shows and explains the logistics/math behind the mystery of card tricks. Dics B are on unusual properties of some numbers. Enjoyed each of the lessons, no fast forward and often LOL in amazement. The professor and his guests appear to be everyday working class folks (except the three kids who help to perform mental math tricks.) As other series in "The Great Courses", it includes the transcript of all the lectures with supplement of exercises and solutions in an easy to read booklet.