Anda suka tantangan?

Kalian tentu sudah mengenal bangun jajargenjang, dan persegi.

Nah....kalau kalian ingin memperkuat ketrampilan dalam membuktikan segiempat-segiempat yang merupakan persegi, di sinilah tempatnya.

Perhatikanlah jajargenjang ABCD berikut.

Kemudian gambarlah persegi-persegi ABGH, ADJI, CDKL, dan BCEF. Tentukan titik-titik pusat dari tiap persegi tadi, yaitu titik potong dari kedua diagonalnya, dan namailah titik pusat itu dengan P, Q, R, dan S seperti pada gambar berikut.

Buktikan bahwa PQRS adalah bangun persegi!

Catatan:

Gunakan konsep-konsep

- Kekongruenan segitiga

- Sudut-sudut yang saling bersuplemen

- Belah ketupat

Nah.....saya jawaban kalian.

Will you be interested on this more number patterns?

A few days ago, I have posted the surprising number patterns on this site. I still have some number patterns which we are able to be interested on it.

What about you?

And, here they are.

Notice (below) how various products of 76,923 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

Another peculiar number is 142,857. When it is multiplied by the numbers 2 through 8, the results are astonishing. Consider the following products and describe the peculiarity.

142,857 . 2 = 285,714

142,857 . 3 = 428,571

142,857 . 4 = 571,428

142,857 . 5 = 714,285

142,857 . 6 = 857,142

You can see symmetries in the products but notice also that the same digits are used in the product as in the first factor. Furthermore, consider the order of the digits. With the exception of the starting point, they are in the same sequence.

Now look at the product, 142,857 . 7 = 999,999. Surprised?

It gets even stranger with the product, 142,857 . 8 = 1,142,856. If we remove the millions digit and add it to the units digit, the original number is formed.

Surprising Number Patterns

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 · 1 = 1

11 · 11 = 121

111 · 111 = 12,321

1,111 · 1,111 = 1,234,321

11,111 · 11,111 = 123,454,321

111,111 · 111,111 = 12,345,654,321

1,111,111 · 1,111,111 = 1,234,567,654,321

11,111,111 · 11,111,111 = 123,456,787,654,321

111,111,111 · 111,111,111 = 12,345,678,987,654,321

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?

Let's be the smart and challenger students

Just I read a mathematics problem, about the sum of an infinite sequence. The problem is described below:
let, A = 1+2+3+4+5+6+7+8+........... (a)
Suppose we have
S = 1+1+1+1+1+1+1+1+1+.......... (b)
If the equations above are added together, then we get
(A+S) = 2+3+4+5+6+7+8+9+10+.......... (c)

But, if (c) is subtracted from (a), then;
A-(A+S) = (1+2+3+4+5+6+7+8+.....) - (2+3+4+5+6+7+8+9+.....)
S = 1
Now, let discuss the last equation that S = 1 or the sum of infinite terms of 1 is equal to 1.
So, what's wrong?
Send your idea.......we are fully waiting your attentions.