小林 幸夫

Exploring of the relationship between a circle and a hyperbola 

Far East Journal of Mathematical Education 25(2) 47-55 2023年11月  査読有り筆頭著者責任著者

Geometric structure of sum of the powers of a natural number 

Far East Journal of Mathematical Education 24(1) 37-44 2023年6月  査読有り筆頭著者責任著者

Proof without words: The sum of the product of two consecutive integers 

Far East Journal of Mathematical Educatio 24(1) 17-20 2023年3月  査読有り筆頭著者責任著者

Using the sum of triangular numbers as the most fundamental number of combinations found using heuristic methods 

European Journal of Pure and Applied Mathematics 15(3) 1237-1253 2022年7月  査読有り筆頭著者責任著者

A pedagogical study of geometric relations between the sums of cubic integer numbers and the sums of square integer numbers with the sums of odd numbers 

European Journal of Pure and Applied Mathematics 15(3) 864-877 2022年7月  査読有り筆頭著者責任著者

Proof without words: a = c ⇒ a = c = a ± c / b ± d in the range of natural numbers 

Far East Journal of Mathematical Education 22(1) 29-32 2022年6月  査読有り筆頭著者責任著者

Proof without words: Relationship between the sum of natural numbers and the sum of the product of two consecutive integer 

Far East Journal of Mathematical Education 22(1) 1-3 2022年2月  査読有り筆頭著者責任著者

Incident position of refracted light beam for reaching a target point 

Far East Journal of Mathematical Education 21(2) 143-154 2021年12月  査読有り筆頭著者責任著者

Proof without Words: Relationship between the sum of triangular numbers, sum of natural numbers, and sum of square numbers 

Far East Journal of Mathematical Education 21(1) 83-91 2021年6月  査読有り筆頭著者責任著者

Proof without words: Relationship between combination ({n}_C_{2))^{2} and sum of cubic numbers 

Far East Journal of Mathematical Education 20(3) 79-82 2020年11月  査読有り筆頭著者責任著者

Pedagogical supplements to mechanical motion in rotating frames 

European Journal of Physics 41(6) 065007 2020年11月  査読有り筆頭著者責任著者

Proof without words: The relation among $\cos (60^{\circ} \pm \theta)$, $\sin (60^{\circ} \pm \theta)$, $\cos (30^{\circ} \pm \theta)$, and $\sin (30^{\circ} \pm \theta)$ 

Far East Journal of Mathematical Education 20(1) 37-38 2020年6月  査読有り筆頭著者責任著者

An illustrated guide to effect of phase to wave phenomena 

Journal of Physics Education (IAPT) 35(4) Article Number 6 (11 pages) 2020年1月  査読有り筆頭著者責任著者

Proof without words: Sum of consecutive odd numbers 

Far East Journal of Mathematical Education 19(1) 59-60 2019年  査読有り筆頭著者責任著者

Proof without words: Relationship between combination $_{n}C_{2}$ and arithmetic numbers from a pedagogical viewpoint 

Far East Journal of Mathematical Education 19(1) 57-58 2019年  査読有り筆頭著者責任著者

Recurrence relation between infinite series and generalised harmonic numbers from a pedagogical viewpoint 

Far East Journal of Mathematical Education 18 101-112 2018年  査読有り筆頭著者責任著者

Proof without words: A sum computed by self-similarity 

College Mathematics Journal 49(1) 10 2018年  査読有り筆頭著者責任著者

Work done by internal forces on a multi body system with constraints 

Journal of Physics Education (IAPT) 34(1) Article Number: 5 (9 pages) 2018年  査読有り筆頭著者責任著者

Proof without words: Product of sum and difference 

Far East Journal of Mathematical Education 17(3) 163 2017年  査読有り筆頭著者責任著者