JURNAL SAINS TERAPAN: REVISI KONSTANTA LINGKARAN BERDASARKAN HUKUM PROYEKSI GESER UNTUK AKURASI INDUSTRI

Penulis: Danang Tyasworo

Topik: Geometri Terapan & Manufaktur Presisi

Kata Kunci: Proyeksi Geser, PHI 3,17157, Akurasi Industri, Geometri Dinamis.

1. ABSTRAK

Dalam matematika Euclidean standar, konstanta π (3,14159) digunakan sebagai rasio keliling terhadap diameter. Namun, dalam aplikasi industri nyata, penggunaan nilai ini sering kali menghasilkan dimensi yang “kekecilan” (defisit), sehingga memerlukan penyesuaian manual. Jurnal ini memperkenalkan nilai PHI = 3,17157 yang diturunkan dari Hukum Proyeksi Geser. Melalui pembuktian empiris menggunakan sampel sudut 90 derajat dan eksperimen pita kertas, ditemukan bahwa nilai ini lebih akurat dalam merepresentasikan panjang material fungsional dibandingkan π tradisional.

2. PENDAHULUAN

Standar industri modern membutuhkan presisi yang tidak hanya benar secara teoretis, tetapi juga tepat secara fisik. Masalah utama dalam penggunaan π standar (3,14) adalah pengabaian terhadap faktor transisi saat material diproyeksikan dari bidang datar ke bidang lengkung. Makalah ini mengusulkan paradigma baru di mana konstanta lingkaran tidak lagi bersifat statis, melainkan dinamis berdasarkan hukum proyeksi.

3. METODOLOGI: HUKUM PROYEKSI GESER

Teori ini didasarkan pada analisis proyeksi pada kuadran 90 derajat. Perhitungan dilakukan dengan mengintegrasikan nilai sinus dan selisih trigonometri (versine) pada titik transisi 45 derajat.

Rumus Dasar (Sampel 90°):

TotalProyeksi=sin90 +(1−cos45)+(1−sin45)

Kalkulasi:

sin90 =1

(1−cos45)=0,29289

(1−sin45)=0,29289

Total = 1,58578

Untuk mendapatkan konstanta linear utuh (PHI), nilai proyeksi 90 derajat ini dikalikan dengan faktor 2:

1,58578×2=3,17156… (dibulatkan menjadi 3,17157)

4. PEMBUKTIAN EMPIRIS (EKSPERIMEN FISIK)

Eksperimen dilakukan menggunakan tabung presisi dan pita kertas tipis untuk meminimalkan variabel ketebalan.

Prosedur: Melilitkan pita kertas pada tabung dan mengukur keliling nyata yang dihasilkan.

Hasil: Eksperimen berulang menunjukkan bahwa keliling fisik material selalu melampaui 3,14×d dan secara konsisten mengarah pada rasio 3,17×d.

Analisis: Selisih ini merupakan hasil dari gaya geser dan ruang transisi yang terjadi saat material mengikuti lengkungan diameter.

5. IMPLIKASI INDUSTRI

Penggunaan PHI 3,17157 memberikan beberapa keuntungan signifikan:

Eliminasi Defisit Material: Menghilangkan celah (gap) pada sambungan komponen melingkar.

Kompensasi Transisi: Secara otomatis menyertakan ruang yang dibutuhkan untuk deformasi material tanpa memerlukan tabel toleransi tambahan.

Standardisasi Baru: Memberikan starting point yang lebih aman bagi desainer CAD/CAM dalam perhitungan flat pattern (bentangan plat).

6. KESIMPULAN

Nilai π 3,14159 mungkin cukup untuk perhitungan matematis murni, namun untuk kepentingan dunia industri yang melibatkan proyeksi material nyata, nilai PHI 3,17157 menawarkan akurasi yang lebih unggul. Hukum Proyeksi Geser berhasil menjembatani celah antara teori geometri dan realitas fisik manufaktur.

APPLIED SCIENCE JOURNAL: REVISING THE CIRCLE CONSTANT BASED ON THE LAW OF SHEAR PROJECTION FOR INDUSTRIAL ACCURACY


Author: Danang Tyasworo
Topic: Applied Geometry & Precision Manufacturing
Keywords: Shear Projection, PHI 3.17157, Industrial Precision, Dynamic Geometry.

  1. ABSTRACT
    In standard Euclidean mathematics, the constant π (3.14159) is used as the ratio of a circle’s circumference to its diameter. However, in real-world industrial applications, using this value often results in “undersized” (deficit) dimensions, requiring manual adjustments. This paper introduces a new constant, PHI = 3.17157, derived from the Law of Shear Projection. Through empirical evidence using a 90-degree projection sample and paper-strip experiments, it is demonstrated that this value more accurately represents the functional material length compared to traditional π.
  2. INTRODUCTION
    Modern industrial standards demand precision that is not only theoretically correct but also physically applicable. The primary issue with using the standard π (3.14) is that it neglects the transition factors when a material is projected from a flat plane to a curved surface. This paper proposes a new paradigm where the circle constant is no longer static, but dynamic, based on the laws of physical projection.
  3. METHODOLOGY: THE LAW OF SHEAR PROJECTION
    This theory is based on projection analysis within a 90-degree quadrant. The calculation integrates sine values and trigonometric variances (versine) at the critical 45-degree transition point.
  4. Fundamental Formula (90° Sample): TotalProjection=sin90+(1−cos45+(1−sin45) The Calculation: sin90=1 (1−cos45)=0.29289 (1−sin45)=0.29289 Total = 1.58578
  5. To obtain the full linear constant (PHI), this 90-degree projection value is multiplied by a factor of 2: 1.58578×2=3.17156… (Standardized to 3.17157)
  6. EMPIRICAL EVIDENCE (PHYSICAL EXPERIMENT)
    Experiments were conducted using precision cylinders and thin paper strips to minimize material thickness variables.
  7. Procedure: Wrapping the paper strip around the cylinder and measuring the actual resulting circumference.
  8. Results: Repeated experiments show that the physical circumference of the material consistently exceeds 3.14×d and aligns toward the ratio of 3.17×d.
  9. Analysis: This variance is the result of shear forces and the “transition space” that occurs when a material is forced to follow a diametrical curve.
  10. INDUSTRIAL IMPLICATIONS
    Utilizing PHI 3.17157 provides several significant advantages: Elimination of Material Deficit: Removes gaps at the joints of circular components.
  11. Transition Compensation: Automatically accounts for the space required for material deformation without needing additional tolerance tables.
  12. New Standardization: Provides a safer “starting point” for CAD/CAM designers in flat-pattern calculations.
  13. CONCLUSION
    While π (3.14159) may suffice for pure mathematical theory, for the practical world of industry involving material projection, PHI 3.17157 offers superior functional accuracy. The Law of Shear Projection successfully bridges the gap between geometric theory and the physical reality of manufacturing

QRIS, an Indonesian Easy Digital Payment Going Global, No, Going Flat Earth ~

Issued by Indonesian Central Bank : Bank Indonesia.

A break through for payment by celluler phone with digital code. It is universally applicable for any country that are willing to join. Has QRIS reached your country?

QRIS is a developed form of QR Code initially founded by a Japanese golden hearted engineer named Masahiro Hara that made his invention free of charge, no license.

https://www.linkedin.com/posts/alvinfsc_masahiro-hara-a-japanese-engineer-at-denso-activity-7406987537673728000-fsCO

Lagu Wajib (Obligatory Songs)

Those songs contain Indonesian nationalism and were written by old time song writers that took role as independence fighters in art field: WR Soepratman, Mutahar, Koesbini, Ibu Soed, C. Simanjuntak, Ismail Marzuki, etc.

Those songs are sung in schools and seem to be all time songs.

A goosebumps song: Tanah Airku written by Ibu Soed, it was globally viral some time ago started from soccer world

Everybody tears.

Lyrics:

Tanah airku tidak kulupakan
‘kan terkenang selama hidupku
Biarpun saya pergi jauh
Tidak ‘kan hilang dari kalbu
Tanahku yang kucintai
Engkau kuhargai

Walaupun banyak negeri kujalani
yang mahsyur permai dikata orang
Tetapi kampung dan rumahku
Di sanalah ku merasa senang
Tanahku tak kulupakan
Engkau kubanggakan

Tanah airku tidak kulupakan
‘kan terkenang selama hidupku
Biarpun saya pergi jauh
Tidak ‘kan hilang dari kalbu
Tanahku yang kucintai
Engkau kuhargai

Translation:

I will not forget my homeland
‘You can remember it for the rest of your life
Even if I go far away
It won’t disappear from my heart
My land that I love
I appreciate you

Even though I have traveled to many countries
which people say is very beautiful
But my village and home
That’s where I feel happy
I will not forget my land
I’m proud of you

I will not forget my homeland
‘You can remember it for the rest of your life
Even if I go far away
It won’t disappear from my heart
My land that I love
I appreciate you

Another song: Indonesia Pusaka written by Ismail Marzuki.

Indonesia recruits Indonesian descendant professional player from Europe

South-African Girl says: Living in Indonesia Feels Like “Family is Everywhere”

Strangers greet and talk to her everywhere ~ without her losing anything afterwards. She never feels alone.

Translation:

Why did you choose to live in Indonesia?

Because people here make me feel ‘having family everywhere’. I learned about the meaning of “home”. It is not about location, instead: “the feeling of being accepted”.