153 (number)

← 152 153 154 →
← 150 151 152 153 154 155 156 157 158 159 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred fifty-three
Ordinal	153rd (one hundred fifty-third)
Factorization	32 × 17
Divisors	1, 3, 9, 17, 51, 153
Greek numeral	ΡΝΓ´
Roman numeral	CLIII, cliii
Binary	100110012
Ternary	122003
Senary	4136
Octal	2318
Duodecimal	10912
Hexadecimal	9916

153 (one hundred [and] fifty-three) is a natural number and integer following 152 and preceding 154.

It is the sum of the first 17 integers, and also the sum of the first five positive factorials. ^[1] It is the 17th triangular number.

In mathematics

The number 153 is the 17th triangular number. The colours show that 153 is also the sum of the first five positive factorials.

The number 153 is associated with the geometric shape known as the Vesica piscis or Mandorla. Archimedes, in his Measurement of a Circle , referred to this ratio (153/265), as constituting the "measure of the fish", this ratio being an imperfect representation of ${\displaystyle 1/{\sqrt {3}}\approx 0.57735}$. ^[2]

As a triangular number, 153 is the sum of the first 17 integers, and is also the sum of the first five positive factorials: ${\displaystyle 1!+2!+3!+4!+5!}$. ^[1]

The number 153 is also a hexagonal number, and a truncated triangle number, meaning that 1, 15, and 153 are all triangle numbers.

The distinct prime factors of 153 add up to 20, and so do the ones of 154, hence the two form a Ruth-Aaron pair.

Since ${\displaystyle 153=1^{3}+5^{3}+3^{3}}$, it is a 3-narcissistic number, and it is also the smallest three-digit number which can be expressed as the sum of cubes of its digits. ^[3] Only five other numbers can be expressed as the sum of the cubes of their digits: 0, 1, 370, 371 and 407. ^[4] It is also a Friedman number, since 153 = 3 × 51.

The Biggs–Smith graph is a symmetric graph with 153 edges, all equivalent.

Another feature of the number 153 is that it is the limit of the following algorithm: ^{[5] [6] [7]}

1. Take a random positive integer, divisible by three
2. Split that number into its base 10 digits
3. Take the sum of their cubes
4. Go back to the second step

An example, starting with the number 84:

${\displaystyle {\begin{aligned}8^{3}+4^{3}&=&512+64&=&576\\5^{3}+7^{3}+6^{3}&=&125+343+216&=&684\\6^{3}+8^{3}+4^{3}&=&216+512+64&=&792\\7^{3}+9^{3}+2^{3}&=&343+729+8&=&1080\\1^{3}+0^{3}+8^{3}+0^{3}&=&1+0+512+0&=&513\\5^{3}+1^{3}+3^{3}&=&125+1+27&=&153\\1^{3}+5^{3}+3^{3}&=&1+125+27&=&153\end{aligned}}}$

There are 153 uniform polypeta that are generated from four different fundamental Coxeter groups in six-dimensional space.

The sum of the first eight Heegner numbers is 153.

In the Bible

Appearance on Lake Tiberias by Duccio, 14th century, showing Jesus and the 7 fishing disciples (with Saint Peter leaving the boat)

The Gospel of John (chapter 21:1–14) includes the miraculous catch of 153 fish as the third appearance of Jesus after his resurrection. ^[8] Augustine of Hippo argued that the significance lay in the fact that 153 is the sum of the first 17 integers (i.e. 153 is the 17th triangular number), representing the combination of divine grace (the seven gifts of the Holy Spirit) and law (the Ten Commandments). ^[9]

References

1. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 140–141.
2. "Measure of the Fish". greatdreams.com.
3. Gupta, Shayam Sunder. "Curious Properties of 153" . Retrieved June 26, 2009.
4. OEIS:A046197
5. Catch of the Day (153 Fishes) at mathpages.com.
6. OEIS:A165330
7. OEIS:A346630
8. Biblegateway John 21:1–14
9. Jason Byassee, Praise Seeking Understanding: Reading the Psalms with Augustine, Wm. B. Eerdmans Publishing, 2007, p. 130, ISBN   0-8028-4012-4.

Bibliography

• Twelftree, Graham H. (1999). "Miracles in the Fourth Gospel". Jesus the Miracle Worker: A Historical and Theological Study. InterVarsity Press. ISBN   9780830815968.
• Flanagan, Neal M. (1992). "John". In Karris, Robert J. (ed.). The Collegeville Bible Commentary: Based on the New American Bible. Liturgical Press. ISBN   9780814622117.
• Edwards, Mark (2008). John Through the Centuries. Wiley Blackwell Bible Commentaries. John Wiley & Sons. ISBN   9781405143196.
• Culpepper, R. Alan (2021). Designs for the Church in the Gospel of John: Collected Essays, 1980–2020. Wissenschaftliche Untersuchungen zum Neuen Testament. Vol. 465. Mohr Siebeck. ISBN   9783161602627.
• Bernard, John Henry (1928). "Introduction". A critical and exegetical commentary on the Gospel According to St John. Vol. 1. Edinburgh: ICC. ISBN   9780567050243.
• Bernard, John Henry (1928). "Notes on the Greek text". A critical and exegetical commentary on the Gospel According to St John. Vol. 2. Edinburgh: ICC. ISBN   9780567050243.
• Grant, Robert M. (2002). "Unusual animals". Early Christians and Animals. Routledge. ISBN   9781134633753.
• Manning, Gary T. Jr. (2004). Echoes of a Prophet: The Use of Ezekiel in the Gospel of John and in Literature of the Second Temple Period. The Library of New Testament Studies. Vol. 270. A&C Black. ISBN   9780567639288.
• Godet, Frédéric Louis; Dwight, Timothy (1893). Commentary on the Gospel of John, with an Historical and Critical Introduction. New York: Funk & Wagnalls.
• Wiarda, Timothy James (1992). "John 21.1–23: Narrative Unity and Its Implications". Journal for the Study of the New Testament. 14 (6): 53–71. doi:10.1177/0142064X9201404604. S2CID   145428133.
• Keener, Craig S. (2010). "Epilogue (21:2–25)". The Gospel of John. Baker Academic. ISBN   9781441237057.
• Hunter, Archibald Macbride (1965). Hunter, Alan (ed.). The Gospel According to John. Cambridge Bible Commentaries on the New Testament. Cambridge University Press. ISBN   9780521092555.

External links

• The Number 153 at The Database of Number Correlations Archived March 20, 2014, at the Wayback Machine