Introduction to the History of Mathematics by Howard Eves

By Howard Eves

This vintage best-seller by means of a well known writer introduces arithmetic heritage to math and math schooling majors. advised essay themes and challenge experiences problem scholars. CULTURAL CONNECTIONS sections clarify the time and tradition during which arithmetic built and advanced. pix of mathematicians and fabric on ladies in arithmetic are of distinctive curiosity.

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T✐♣❧② t❤❡ ❢r❛❝t✐♦♥s. 60% ❘❡♣❧❛❝❡ 1 100 ✇✐t❤ t❤❡ % s②♠❜♦❧. 75 ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ 1 100 . 75 · 100 · = 75 · = 75% 1 100 ▼✉❧t✐♣❧② t❤❡ ❞❡❝✐♠❛❧ ❜② ✶✳ 1 100 ❘❡♣❧❛❝❡ 1 100 ✇✐t❤ t❤❡ ✪ s②♠❜♦❧. 623% 1 100 1 100 ◆♦t✐❝❡ t❤❛t t❤❡ ❞❡❝✐♠❛❧ ♣♦✐♥t ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ♥✉♠❜❡r ❤❛s ❜❡❡♥ ♠♦✈❡❞ t♦ t❤❡ r✐❣❤t ✷ ♣❧❛❝❡s✳ ✶✳✽✳✼ ❈♦♥✈❡rt✐♥❣ ❆ P❡r❝❡♥t ❚♦ ❆ ❉❡❝✐♠❛❧ ❲❡ ❝❛♥ s❡❡ ❤♦✇ ❛ ♣❡r❝❡♥t ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ ❞❡❝✐♠❛❧ ❜② ❛♥❛❧②③✐♥❣ t❤❡ ♠❡t❤♦❞ t❤❛t ✶✷✪ ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ ❞❡❝✐♠❛❧✳ ❲❡ ♥❡❡❞ t♦ ✐♥tr♦❞✉❝❡ 1 100 . 12% 1 100 1 100 . = 12 · = 12 100 ▼✉❧t✐♣❧② t❤❡ ❢r❛❝t✐♦♥s.

T❤❡ ♥✉♠❡r❛t♦rs ❛♥❞ ♣❧❛❝❡ t❤❡ s✉♠ ♦✈❡r ✼. = 3+2 7 = 5 7 ❊①❛♠♣❧❡ ✶✳✸✶ 7 9 7 9 − 49 . − 4 9 ❚❤❡ ❞❡♥♦♠✐♥❛t♦rs ❛r❡ t❤❡ s❛♠❡. ❙✉❜tr❛❝t ✹ ❢r♦♠ ✼ ❛♥❞ ♣❧❛❝❡ t❤❡ ❞✐✛❡r❡♥❝❡ ♦✈❡r ✾. = 7−4 9 = 3 9 = 1 3 ✶✳✻✳✽ ❋r❛❝t✐♦♥s ❝❛♥ ♦♥❧② ❜❡ ❛❞❞❡❞ ♦r s✉❜tr❛❝t❡❞ ❝♦♥✈❡♥✐❡♥t❧② ✐❢ t❤❡② ❤❛✈❡ ❧✐❦❡ ❞❡♥♦♠✐♥❛t♦rs✳ ❋r❛❝t✐♦♥s ✇✐t❤ ❯♥❧✐❦❡ ❉❡♥♦♠✐♥❛t♦rs ❚♦ ❛❞❞ ♦r s✉❜tr❛❝t ❢r❛❝t✐♦♥s ❤❛✈✐♥❣ ✉♥❧✐❦❡ ❞❡♥♦♠✐♥❛t♦rs✱ ❝♦♥✈❡rt ❡❛❝❤ ❢r❛❝t✐♦♥ t♦ ❛♥ ❡q✉✐✈❛❧❡♥t ❢r❛❝t✐♦♥ ❤❛✈✐♥❣ ❛s t❤❡ ❞❡♥♦♠✐♥❛t♦r t❤❡ ❧❡❛st ❝♦♠♠♦♥ ♠✉❧t✐♣❧❡ ♦❢ t❤❡ ♦r✐❣✐♥❛❧ ❞❡♥♦♠✐♥❛t♦rs✳ ❚❤❡ ❧❡❛st ❝♦♠♠♦♥ ♠✉❧t✐♣❧❡ ♦❢ t❤❡ ♦r✐❣✐♥❛❧ ❞❡♥♦♠✐♥❛t♦rs ✐s ❝♦♠♠♦♥❧② r❡❢❡rr❡❞ t♦ ❛s t❤❡ ❧❡❛st ❝♦♠♠♦♥ ❞❡♥♦♠✐♥❛t♦r ✭▲❈❉✮✳ ❙❡❡ ❙❡❝t✐♦♥ ❘✳✸ ✭❙❡❝t✐♦♥ ✶✳✹✮ ❢♦r t❤❡ t❡❝❤♥✐q✉❡ ♦❢ ✜♥❞✐♥❣ t❤❡ ❧❡❛st ❝♦♠♠♦♥ ♠✉❧t✐♣❧❡ ♦❢ s❡✈❡r❛❧ ♥✉♠❜❡rs✳ ✶✳✻✳✾ ❙❛♠♣❧❡ ❙❡t ❉ ❋✐♥❞ ❡❛❝❤ s✉♠ ♦r ❞✐✛❡r❡♥❝❡✳ ❊①❛♠♣❧❡ ✶✳✸✷ 1 6 { + 34 .

3 4 ❚❤❡ ❞✐✈✐s♦r ✐s 3 4 4 ✳ ■ts r❡❝✐♣r♦❝❛❧ ✐s 3 . 1 4 3 · 3 1·4 3·3 4 9 = = = ❊①❛♠♣❧❡ ✶✳✷✽ 3 8 3 8 ÷ 54 . ÷ 5 4 ❚❤❡ ❞✐✈✐s♦r ✐s = 3 8 = 3 2·2 2·2·2 · 5 3 · )2 5· )2 )2 · )2 · 2 3·1 2·5 3 10 = = = · 5 4 4 ✳ ■ts r❡❝✐♣r♦❝❛❧ ✐s 5 . 4 5 ✷ ✐s ❛ ❝♦♠♠♦♥ ❢❛❝t♦r✳ ❊①❛♠♣❧❡ ✶✳✷✾ 5 6 5 6 ÷ ÷ 5 12 . 5 12 ❚❤❡ ❞✐✈✐s♦r ✐s = 5 6 = = 5 2·2·3 2·3 · 5 )5 )2 · 2 · )3 · )2 · )3 )5 1·2 1 = 2 = · 12 5 5 12 12 ✳ ■ts r❡❝✐♣r♦❝❛❧ ✐s 5 . ✷✺ ✶✳✻✳✻ ❆❞❞✐t✐♦♥ ❛♥❞ ❙✉❜tr❛❝t✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ❋r❛❝t✐♦♥s ✇✐t❤ ▲✐❦❡ ❉❡♥♦♠✐♥❛t♦rs ❚♦ ❛❞❞ ✭♦r s✉❜tr❛❝t✮ t✇♦ ♦r ♠♦r❡ ❢r❛❝t✐♦♥s t❤❛t ❤❛✈❡ t❤❡ s❛♠❡ ❞❡♥♦♠✐♥❛t♦rs✱ ❛❞❞ ✭♦r s✉❜tr❛❝t✮ t❤❡ ♥✉♠❡r❛t♦rs ❛♥❞ ♣❧❛❝❡ t❤❡ r❡s✉❧t✐♥❣ s✉♠ ♦✈❡r t❤❡ ❝♦♠♠♦♥ ❞❡♥♦♠✐♥❛t♦r✳ ❘❡❞✉❝❡ ✐❢ ♣♦ss✐❜❧❡✳ ❈❆❯❚■❖◆ ❆❞❞ ♦r s✉❜tr❛❝t ♦♥❧② t❤❡ ♥✉♠❡r❛t♦rs✳ ❉♦ ♥♦t ❛❞❞ ♦r s✉❜tr❛❝t t❤❡ ❞❡♥♦♠✐♥❛t♦rs✦ ✶✳✻✳✼ ❙❛♠♣❧❡ ❙❡t ❈ ❋✐♥❞ t❤❡ ❢♦❧❧♦✇✐♥❣ s✉♠s✳ ❊①❛♠♣❧❡ ✶✳✸✵ 3 7 3 7 + 27 .

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