Today's example is also about actual solution of Cube root using abacus. The calculation becomes more complicated than previous example.
Today's example is simple - basic Triple-root method, root is 3-digits case and requires excessive root modification. Please check the Theory page for your reference.
Cube root methods: Triple-root method, constant number method, 3a^2 method, 1/3-division method, 1/3-multiplication table method, 1/3-multiplication table alternative method, Multiplication-Subtraction method, 3-root^2 method, Mixing method, Exceed number method, Omission Method, etc.
Abacus steps to solve Cube root of 5,735,339
(Answer is 179)
"1st group number" is the left most numbers in the 3-digits groups of the given number for cube root calculation. Number of groups is the number of digits of the Cube root.
5,735,339 -> (5|735|339): 5 is the 1st group number. The root digits is 3.
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Step 1: Set 5735339. First group is 5.
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Step 2: Cube number smaller than 5 is 1=1^3. Place 1 on E as 1st root.
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Step 3: Place 5-1=4 on I. ( -a^3)
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Step 4: Place Triple root 3x1=3 on B.
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Step 5: Repeat division by triple root 3 until 4th digits next to 1st root. (/3a)
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Step 6: 4/3=1 remainder 1. Place 1 on G.
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Step 7: Place remainder 1 on I.
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Step 8: 17/3=5 remainder 2.
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Step 9: Place 5 on H.
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Step 10: Place remainder 02 on IJ.
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Step 11: 23/3=7 remainder 2.
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Step 12: Place 7 on I.
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Step 13: Place remainder 02 on JK.
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Step 14: Place 8 on F as 2nd root according to the calculation rule.
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Step 15: Divide 15 on GH by 2nd root. 15/8=1 remainder 7.
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Step 16: Place 07 on GH.
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Step 17: Subtract 2nd root^2 from 77 on HI. ( -b^2)
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Step 18: It means place 77-8^2=13 on HI.
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Step 19: Multiply triple root=3 by remainder 13 on HI. 3X13=39
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Step 20: Set 00 on HI.
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Step 21: Add 39 to 0002 on HIJK. 39+2=41
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Step 22: It means place 0041 on HIJK.
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Step 23: Cannot subtract 8^3 from 415 on JKL. 8 is excessive root. Subtract 1 from 8. Place 7 on F.
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Step 24: Give back 10+8+7=25 on HI.
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Step 25: Multiply triple root=3 by remainder 25 on HI. 3X25=75
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Step 26: Set 00 on HI.
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Step 27: Add 75 to 041 on IJK.
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Step 28: It means place 041+75=116 on IJK.
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Step 29: Subtract 2nd root^3 from 1165 on IJKL. 1165-7^3=822 ( -b^3)
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Step 30: Place 0822 on IJKL.
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Step 31: Add 3x2nd root to triple root 30. Place 30+21=51 on BC.
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Step 32: Repeat division by triple root 51 from J.
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Step 33: 82/51=1 remainder 31. Place 1 on H. Place remainder 31 on JK.
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Step 34: 312/51=6 remainder 6. Place 6 on I.
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Step 35: Place remainder 006 on JKL.
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Step 36: 63/51=1 remainder 12. Place 1 on J.
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Step 37: Place remainder 12 on LM.
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Step 38: 123/51=2 remainder 21. Place 2 on K.
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Step 39: Place remainder 021 on LMN.
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Step 40: Divide 161 by current root 17. 161/17=9 remainder 8.
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Step 41: Place 9 on G as 3rd root.
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Step 42: Place remainder 008 on HIJ.
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Step 43: Subtract 3rd root^2 from 82. 82-9^2=1 ( -c^2)
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Step 44: Place 01 on JK.
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Step 45: Multiply triple root=51 by remainder 01 on JK. 51X1=51
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Step 46: Set 00 on JK.
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Step 47: Add 51 to 21 on MN. 21+51=72.
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Step 48: Place 72 on MN.
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Step 49: Subtract 3rd root^3 from 729 on MNO. ( -c^3)
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Step 50: Place 729-9^3=000 on MNO.
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Step 51: Cube root of 5735339 is 179.
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Final state: Answer 179
Today's example is also about actual solution of Cube root using abacus. The calculation becomes more complicated than previous example.
Today's example is simple - basic Triple-root method, root is 4-digits case. Please check the Theory page for your reference.
Cube root methods: Triple-root method, constant number method, 3a^2 method, 1/3-division method, 1/3-multiplication table method, 1/3-multiplication table alternative method, Multiplication-Subtraction method, 3-root^2 method, Mixing method, Exceed number method, Omission Method, etc.
Abacus steps to solve Cube root of 12,895,213,625
(Answer is 2,345)
"1st group number" is the left most numbers in the 3-digits groups of the given number for cube root calculation. Number of groups is the number of digits of the Cube root.
12,895,213,625 -> (12|895|213|625): 12 is the 1st group number. The root digits is 4.
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Step 1: Set 12895213625. First group is 12.
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Step 2: Cube number smaller than 12 is 8=2^3. Place 2 on E as 1st root.
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Step 3: Place 12-8=04 on HI. ( -a^3)
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Step 4: Place Triple root 3x2=6 on B.
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Step 5: Repeat division by triple root 6 until 4th digits next to 1st root. ( /3a)
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Step 6: 48/6=8 remainder 0. Place 8 on G.
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Step 7: Place remainder 00 on IJ.
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Step 8: 9/6=1 remainder 3.
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Step 9: Place 1 on I.
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Step 10: Place remainder 3 on K.
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Step 11: Divide 0 on F by current root 2.
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Step 12: Get 3 as 2nd root and place it on F.
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Step 13: Place 8-2x3=2 on H.
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Step 14: Subtract 2nd root^2 from 21 on HI. ( -b^2)
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Step 15: Place 21-3^2=12 on HI.
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Step 16: Multiply triple root 6 by remainder 12 on HI. 6X12=72
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Step 17: Replace 12 by 00 on HI.
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Step 18: Add 72 to 03 on JK.
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Step 19: It means place 03+72=75 on JK.
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Step 20: Subtract 2nd root^3 from 755 on JKL. ( -b^3)
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Step 21: It means place 755-3^3=728 on JKL.
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Step 22: Add 3x2nd root to triple root on BC.
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Step 23: Place 60+3x3=69 on BC.
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Step 24: Repeat division by triple root 69 until fixed position.
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Step 25: 72/69=1 remainder 3. Place 1 on H.
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Step 26: Place remainder 03 on JK.
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Step 27: 38/69=0 remainder 38
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Step 28: Place 0 on I. Place remainder 38 on KL.
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Step 29: 382/69=5 remainder 37
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Step 30: Place 5 on J.
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Step 31: Place remainder 037 on JKL.
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Step 32: 371/69=5 remainder 26
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Step 33: Place 5 on K.
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Step 34: Place remainder 026 on LMN.
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Step 35: Divide 105 on HIJ by current root 23. 105/23=4 remainder 13
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Step 36: Place 4 on G as 3rd root.
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Step 37: Place remainder 013 on HIJ.
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Step 38: Subtract 3rd root^2 from 135 on IJK. ( -c^2)
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Step 39: Place 135-4^2=119 on IJK.
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Step 40: Multiply triple root 69 by remainder 119 on IJK. 69X119=8211
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Step 41: Replace 119 by 000 on IJK.
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Step 42: Add 8211 to 0026 on KLMN.
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Step 43: It means place 0026+8211=8237 on KLMN.
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Step 44: Subtract 3rd root^3 from 73 on NO. ( -c^3)
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Step 45: Place 73-4^3=09 onNO.
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Step 46: Add 3x3rd root to triple root on BCD.
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Step 47: Place 690+3x4=702 on BCD.
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Step 48: Repeat division by triple root 702 until fixed position.
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Step 49: 823/702=1 remainder 121. Place 1 on I.
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Step 50: Place remainder 121 on KLM.
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Step 51: 1210/702=1 remainder 508
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Step 52: Place 1 on J.
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Step 53: Place remainder 0508 on KLMN.
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Step 54: 5089/702=7 remainder 175
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Step 55: Place 7 on K.
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Step 56: Place remainder 0175 on LMNO.
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Step 57: 1756/702=2 remainder 352
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Step 58: Place 2 on L.
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Step 59: Place remainder 0352 on MNOP.
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Step 60: 3522/702=5 remainder 12
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Step 61: Place 5 on M.
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Step 62: Place remainder 0012 on NOPQ.
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Step 63: Divide 1172 on JKLM by current root 234. 1172/234=5 remainder 2
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Step 64: Place 5 on G as 4th root.
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Step 65: Place remainder 0002 on IJKL.
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Step 66: Subtract 4th root^2 from 25 on LM. ( -d^2)
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Step 67: Place 25-5^2=00 on LM.
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Step 68: Subtract 4th root^3 from 125 on PQR. (-d^2)
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Step 69: Place 125-5^3=000 on PQR.
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Step 70: Cube root of 12895213625 is 2345.
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Final state: Answer 2345
そして陽子や中性子はクォークとグルーオンで構成されている。そのことはCERNのLHC加速器が建設される前、LEP (The Large Electron-Positron Collider)という装置だったときに行われた実験によって明らかになっていた。この２つの実験結果は量子色力学（QCD）によって解釈可能になっていたのだ。
第３部からは標準理論が示しているU(1)、SU(2)、SU(3)などのゲージ対称性の話から始まる。U(1)、SU(2)、SU(3)はそれぞれ電磁気力、弱い力、強い力に対応し、「リー群」という対称性をもった数学的表現であらわされる。これらの対称性を含むより大きな対称性が見つかるのだろうか？重力理論をも含む「超対称性」を見つけることができるのだろうか？この点については（本書執筆時点では稼働していない）CERNのLHC (The Large Hadron Collider)への期待が語られている。ご存知のようにこの実験施設では「ヒッグス粒子」が検出され、2012年7月4日に発表され標準理論の正しさが裏付けられ、質量の起源の残りの部分が解明された。（参考記事：「祝！：ヒッグス粒子発見」）
本書の邦題「物質のすべては光」は、一般の人にはわかりにくいかもしれない。原題は「The Lightness of Being」（存在の軽さ）である。Lightness（軽さ）とLight（光）をかけていること、そして原題は「The Unbearable Lightness of Being」（「存在の耐えられない軽さ」）という小説をもじったものである。
A very exciting LIGO-Virgo Observing run is drawing to a close August 25
25 August 2017 -- The Virgo and LIGO Scientific Collaborations have been observing since November 30, 2016 in the second Advanced Detector Observing Run ‘O2’ , searching for gravitational-wave signals, first with the two LIGO detectors, then with both LIGO and Virgo instruments operating together since August 1, 2017. Some promising gravitational-wave candidates have been identified in data from both LIGO and Virgo during our preliminary analysis, and we have shared what we currently know with astronomical observing partners. We are working hard to assure that the candidates are valid gravitational-wave events, and it will require time to establish the level of confidence needed to bring any results to the scientific community and the greater public. We will let you know as soon we have information ready to share.
On 18 August, astronomer J. Craig Wheeler of the University of Texas at Austin began the public rumour mill when he tweeted, “New LIGO. Source with optical counterpart. Blow your sox off!” An hour later, astronomer Peter Yoachim of the University of Washington in Seattle tweeted that LIGO had seen a signal with an optical counterpart (that is, something that telescopes could see) from a galaxy called NGC 4993, which is around 40 million parsecs (130 million light years) away in the southern constellation Hydra. “Merging neutron-neutron star is the initial call”, he followed up. Some astronomers who do not want to be identified say that rumours had been privately circulating before Wheeler’s and Yoachim’s tweets.
その後、WheelerとYoachimはコメントを取り下げ、Wheelerは「Right or wrong, I should not have sent that tweet. LIGO deserves to announce when they deem appropriate. Mea culpa,（それが正しかろうが間違いであろうが、私はあのようなツイートをすべきでなかった。適切だと判断した段階で、LIGOから発表するのが正しいことだ。謝罪させていただきます。）」とツイートしている。
Do you know we can calculate 3rd root, 5th root using standard calculator with Square Root key [SQRT]? Following is the method how to do it
This is the calculator of the Mr.Calculator abacus.
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As shown above, Memory Clear is assigned to [CM] key and Memory Read (Recall) key is assigned to [RM] key. In this article we use [MC] and [MR] respectively as used by the standard calculator.
Some calculator has [MRC] key instead of [MC] and [MR] key. If you press [MRC] key once, it means [MR] and If you press [MRC] key twice, it means [MC].
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For example, 4th root is calculated by Square root twice and 6th root is calculated by multiplication of square root and cube root. It is enough to know the calculation method of N-th root where N is prime number greater than 2.
3rd root of A (Cube root of A)
[MC] A [M+] [SQRT] [SQRT]
[x] [MR] [=] [SQRT] [SQRT]
[x] [MR] [=] [SQRT] [SQRT]
Repeat until convergence.
5th root of A
[MC] A [M+] [SQRT] 3 times
[x] [=] [=] [x] [MR] [=] [SQRT] 3 times
[x] [=] [=] [x] [MR] [=] [SQRT] 3 times
Repeat until convergence.
7th root of A
[MC] A [M+] [SQRT] 3 times
[x] [MR] [=] [SQRT] 3 times
[x] [MR] [=] [SQRT] 3 times
Repeat until convergence.
11th root of A
[MC] A [M+] [SQRT] 4 times
[x] [=] 4 times [x] [MR] [=] [SQRT] 4 times
[x] [=] 4 times [x] [MR] [=] [SQRT] 4 times
Repeat until convergence.
13th root of A
[MC] A [M+] [SQRT] 4 times
[x] [=] [=] [x] [MR] [=] [SQRT] 4 times
[x] [=] [=] [x] [MR] [=] [SQRT] 4 times
Repeat until convergence.
Let's confirm the methods with actual value. I show you only value transition and the value calculated with iPhone's scientific calculator.
3rd root of 10
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5th root of 10
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7th root of 10
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11th root of 10
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13th root of 10
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As a matter of fact, we can calculate N-th root using calculator WITHOUT [SQRT] key. I'll show you the method in the next article.
I explained how to calculate N-th root using calculator with [SQRT] key in the previous article. You can also calculate N-th root using calculator WITHOUT [SQRT] key. Following is the method how to do it
This is the calculator of the Mr.Calculator abacus.
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As shown above, Memory Clear is assigned to [CM] key and Memory Read (Recall) key is assigned to [RM] key. In this article we use [MC] and [MR] respectively as used by the standard calculator.
Some calculator has [MRC] key instead of [MC] and [MR] key. If you press [MRC] key once, it means [MR] and If you press [MRC] key twice, it means [MC].
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For example, 4th root is calculated by Square root twice and 6th root is calculated by multiplication of square root and cube root. It is enough to know the calculation method of N-th root where N is prime number greater than 1.
Note that [/] is the Division key in the explanation below.
2nd root of A (Square root)
Input approximate value of 2nd root of A.
[MC][M+]A
[/][MR] Enter 1 time.
[=]
[+][MR] Enter 1 time
[=][/][2][=]
Repeat from the line [MC] until value does not change.
3rd root of A (Cube root)
Input approximate value of 3rd root of A.
[MC][M+]A
[/][MR] Enter 2 times
[=]
[+][MR] Enter 2 times.
[=][/][3][=]
Repeat from the line [MC] until value does not change.
5th root of A
Input approximate value of 5th root of A.
[MC][M+]A
[/][MR] Enter 4 times.
[=]
[+][MR] Enter 4 times.
[=][/][5][=]
Repeat from the line [MC] until value does not change.
7th root of A
Input approximate value of 7th root of A.
[MC][M+]A
[/][MR] Enter 6 times.
[=]
[+][MR] Enter 6 times.
[=][/][7][=]
Repeat from the line [MC] until value does not change.
11th root of A
Input approximate value of 11th root of A.。
[MC][M+]A
[/][MR] Enter 10 times.
[=]
[+][MR] Enter 10 times.
[=][/][11][=]
Repeat from the line [MC] until value does not change.
13th root of A
Input approximate value of 13th root of A.
[MC][M+]A
[/][MR] Enter 12 times.
[=]
[+][MR] Enter 12 times.
[=][/][13][=]
Repeat from the line [MC] until value does not change.
You can apply to all N where N is the natural numbers greater than 1.
N-th root of A
Input approximate value of N-th root of A.
[MC][M+]A
[/][MR] Enter N-1 times.
[=]
[+][MR] Enter N-1 times.
[=][/][N][=]
Repeat from the line [MC] until value does not change.
Let's confirm the methods with actual value. I show you only value transition and the value calculated with iPhone's scientific calculator.
If Freddie Mercury is alive, he is 71 years old. I enjoyed the Queeness Live in Tokyo with my friend last Saturday.
Original Queen are a British rock band that formed in London in 1970 and made a great sucess in England, the U.S., Japan and all over the world. But I found many young people do not know the band. Some of them know only their music.
The "Queeness" is the most famous tribute band of Queen. Its leader Freddie Eto (Vocal) is one of my important friend I worked together in early 1990 in the company I work now.
Queeness is introduced in the next video - Japanese TV variety show several years ago. In the video, Brian May (of original Queen) sent a letter to Queeness and said "Thank you very much for succeeding our music." - It means Queeness is admitted by original Queen. Apart from Freddie Eto's unique personality, Queeness music attracts audiences so strong by their excellent sound and performance.
Live in Tokyo!: Queeness ”You Want It All?” Japan Tour 2017
Date: September 2nd (Sat), Open 17:00 Start 18:00
Place: Shinjuku ReNY (Island Hall)
Ryuichi Yamamura (Jazz musician) as John Deacon is another friend of mine. I came to know him when I went to the "Jazz live played by Takako Inaba" on Feb 2006.
This is coincidence and surprising. Mr. Yamamura is the junior fellow of Freddie Eto during his high school and I didn't know that Mr. Yamamura is a member of Queeness.
The friend I invited to the live was born beyond the Queen's prime. She was devoted to Queen when she was in elementary school by her elder brother's influence. She knows almost everything about Queen. I think this is the only person I can invite to the live. This is the 3rd time invitation.
We were worried about big typhoon No.15 and fortunately it changed direction to off-island of Japan. Weather recovered and we could receive soft sunlight and fresh air in the afternoon.
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The music live house - Shinjuku ReNY is very big and its capacity is 800 audiences.
We have to keep standing from begin to end. I don't care about it because I walk every night for training. I met 2 old-friends in the live house.
The time of my friend's arrival was unpredictable. She had a job in Ginza and came to the appointment spot 30 minutes before the hall open. No problem! We could talk recent events and future plan until the live start.
10 years have passed since I got to know her. Long and fine friendship made us think about what had happened to each of us during the years we didn't have a chance to talk. There are many things to tell, but I could not bring back to memory in a short period of time. I will tell her next time.
Live started at 6pm and we enjoyed about 30 songs. It ended around 8:30pm. My friend knows all songs and I know only half of them. She said after the previous live that "Roger's voice is almost same as original singer." and "Not only his voice, but also his looking is same as Roger." she said this time.
She is a great cinema maven. She likes Queen's "Brighton Rock" which was used for the catastasis at the end of the movie "Baby Driver". She expects the song is in the
playlist which was not played in the live in 2014. She was satisfied to the song started in the middle
of the live.
Between the songs, Freddie Eto tells his dream to hold a Queeness live in the big and most famous Budokan Hall and he requests audiences in English. "I ask you each of you here to take 50 friends for the Budokan live! Then your ticket is free!" He asked Brian for Japanese translation. "I don't want to translate about such pyramid style selling to the audiences." said Brian. But he finished translation at the next moment.
We were aloud to take photos and movies without flash. But we can upload only photos to internet. If you want to watch Queen movie, search from YouTube.
I realized at many parents and children in the live house compared with the previous live in 2014. I am sure that the great Queen's music is inherited to next generation. Next videos are the kids and elders reaction to Queen's music.
We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena. Usually such a beautiful generalization is found to stem from a single deep underlying principle. Nevertheless, in this case there does not appear to be any such profound implication. We have to understand the “rule” as the combined effects of two quite separate phenomena.
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