ARE ALL NUMBERS EQUAL?

The title of this charmer is clearly preposterous! But as you will see from the demonstration below, such may not be the case. Present this demonstration line by line and let you draw your own conclusions.

We shall begin with the easily accepted equation:

Each succeeding row can be easily justified with elementary algebra. There is nothing wrong with the algebra. See if you can find the flaw.

When x = 1, the numbers 1,2,3,4,....,n are each equal to 0/0, which would make them all equal to each other. Of course, this cannot be true. For this reason, we define 0/0 to be meaningless. To define something to make things meaningful or consistent is what we do in mathematics to avoid ridiculous statements, as was the case here. Be sure to stress this point before leaving this unit.

SEJARAH ANGKA, JARI TANGAN, DAN JARI KAKI

Bilangan Hindu-Arab, seperti 1, 2, 3, 4, 5, 6, 7, 8, 9, berawal dari Hindustan dan dirancang seiring dengan sistem desimal. kata desimal berawal dari kata sepersepuluh. Sistem Hindu-Arab merupakan sistem posisi, yang berarti bahwa urutan bilangan yang kamu tulis menjadi penting. Bilangan 35 berbeda dari bilangan 53 karena angka 3 pada 35 wewakili tiga puluhan dan 3 pada 53 mewakili tiga satuan.

Alasan utama manusia mengembangkan sistem desimal atau sistem dasar sepuluh karena manusia biasanya memiliki sepuluh jari tangan dan sepuluh jari kaki. Bisa jadi, ini merupakan sistem dasar dua puluh atau sistem dasar lima - seperti yang dimiliki orang Babilonia. Namun, kira-kira dari tahun 1700 SM sampai 500 M, kebanyakan ilmuwan menggunakan sistem dasar enam puluh. Penggunaan enam puluh sebagai dasar muncul karena jumlah hari dalam setahun diperkirakan 360 hari, dan enampuluh merupakan pembagi yang paling tepat untuk 360. Peninggalan sistem dasar enam puluh bisa ditemukan pada hitungan menit dan detik pada jam. Bisakah kamu membayangkan harus mengingat enampuluh angka berbeda?

Simbol-simbol yang digunakan pada sistem-sistem terdahulu mewakili sesuatu: satu untuk ini, dua untuk itu, dan seterusnya. Untuk waktu yang lama, belum adad angka atau simbol yang digunakan untuk mewakili nol. Simbol pertama untuk nol  (berbentuk W terbalik) belum dikenal sampai sekitar 300 SM. Sebelumnya, untuk menunjukkan nol. penulis akan memberi sela. Cara ini sangat tidak efektif. Kadang-kadang penulis lupa memberi sela, dan penulis yang tidak hati-hati mungkin tidak memberi cukup sela. Lagi pula, belum ada cara yang jelas untuk menunjukkan lebih dari satu nol!

THE AMAZING OF THE VARIOUS PRODUCTS OF 76,923

When 76,923 is multiplied by certain numbers, then it will yield numbers in the same order but with a different starting point. Here the first digit of the product goes to the end of the number to form the next product. Otherwise, the order of the digits is intact.

76,923 ·   1 = 076,923
76,923 . 10 = 769,230
76,923 .   9 =  692,307
76,923 . 12  = 923,076
76,923 .   3 = 230,769
76,923 .   4 =  307,692

Notice (below) how various products of 76,923 yield different numbers from those above, yet again, in the same order but with a different starting point. Again, the first digit of the product goes to the end of the number to form the next product. Otherwise, the order of the digits is intact.

76,923 .  2 = 153,846
76,923 .  7 = 538,461
76,923 .  5 = 384,615
76,923 . 11 = 846,153
76,923 .  6 = 461,538
76,923 .  8 = 615,384

SURPRISING NUMBER PATTERN II

Dear my lovely students,

What do you feel about mathematics? Do you think that mathematics is difficult? Why?

Meanwhile, maybe, some students say that mathematics is fun.

Well…..

I think we have to appreciate all the opinions. But, now, I will show that mathematics is fun. I have some amazing with mathematics. And I hope it will change all the frights to the full of fun.

Actually, there are times/multiplications when the charm of mathematics lies in the surprising nature of its number system. There are not many words needed to demonstrate this charm. It is obvious from the patterns attained.

Look, enjoy, and spread these amazing properties. Let you appreciate the patterns and, if possible, try to look for an “explanation” for this. Most important is that you can get an appreciation for the beauty in these number patterns.

1 · 8 + 1 = 9

12 · 8 + 2 = 98

123 · 8 + 3 = 987

1,234 · 8 + 4 = 9,876

12,345 · 8 + 5 = 98,765

123,456 · 8 + 6 = 987,654

1,234,567 · 8 + 7 = 9,876,543

12,345,678 · 8 + 8 = 98,765,432

123,456,789 · 8 + 9 = 987,654,321

Well…..

What do you say about the patterns above? I think it will be better if you would like to give some comments, ok?